In the Internet era, the demand for transmission speed and transmission capacity of optical communication systems has increased significantly. Electro-optic modulators for optical communication systems are developing towards high speeds. Traditional silicon-based electro-optic modulators have a slow response speed. Graphene has excellent optical and electrical properties and is compatible with Complementary Metal Oxide Semiconductor (CMOS) processes. Combining graphene with silicon materials can improve the response speed of electro-optic modulators. At the same time, wide bandwidth, high extinction ratio, low insertion loss, and low energy consumption are the development trends of graphene electro-optic modulators. On the other hand, to meet the needs of optical communication systems, multiplexing technologies such as mode division multiplexing are used to increase the communication capacity. The research on a single-function optical communication device has gradually matured, and the combination of different devices to form an integrated device has become a research hotspot in recent years. The combination of electro-optic modulation and mode division multiplexing technology can improve the transmission speed and transmission capacity of optical communication systems. With the continuous advancement of science and technology, optical interconnection has attracted widespread attention due to its advantages of high speed, wide bandwidth and large capacity, and various integrated devices have emerged as the times require. Among them, the integrated device for electro-optic modulation and mode division multiplexing has shortcomings such as small transmission capacity and low transmission speed. Meanwhile, different devices are difficult to integrate due to differences in materials and structures.A three-channel integrated device for graphene electro-optic modulation and mode division multiplexing is proposed, which consists of a one-dimensional photonic crystal nanobeam cavity electro-optic modulation module covered by a single-layer graphene and nanowire waveguides mode division multiplexing module. The electro-optic modulator is composed of a one-dimensional photonic crystal nanobeam cavity, a nanowire waveguide, and a silicon plate. Combining the curved waveguide with the straight waveguide improves the coupling efficiency of the one-dimensional photonic crystal nanobeam cavity and the nanowire waveguides. A layer of Al₂O₃ is covered on top of the silicon plate and the one-dimensional photonic crystal nanobeam cavity, and a single-layer graphene is added on top of the Al₂O₃. The electrodes on graphene serve as anodes, and the electrodes on silicon plates serve as cathodes. Applying a voltage changes the chemical potential of graphene, enabling modulation of specific wavelengths. According to the principle of mode matching, the mode division multiplexer adopts an asymmetric directional coupling nanowire waveguides structure. In the phase matching region, the fundamental modes in the single-mode waveguide are converted into the higher-order modes in the multi-mode waveguide, realizing the conversion of different modes. The TE₀ modes are output from the same port in the form of TE₀ modes, TE₁ modes and TE₂ modes through the graphene electro-optic modulator and mode division multiplexer, achieving the functions of electro-optic modulation and mode division multiplexing.The performance parameters of the three-channel integrated device for graphene electro-optic modulation and mode division multiplexing are analyzed using the three-dimensional finite-difference time-domain method. During the production and preparation of the devices, the influence of process errors on the performance of the devices needs to be considered. Therefore, important structural parameters of the graphene electro-optic modulator and nanowire waveguides mode division multiplexer are selected for tolerance analysis, respectively. At the wavelength of 1 570 nm, when the voltage is 0 V, the incident light is not coupled with the one-dimensional photonic crystal nanobeam cavity and can be transmitted along the waveguide. The modulator is in the on-state. When the voltage is 3.8 V, the chemical potential of graphene changes, resulting in a change in the equivalent refractive index of the material. Therefore, the resonance wavelength of the one-dimensional photonic crystal nanobeam cavity is shifted to match the target wavelength (1 570 nm), and the incident light is coupled into the microcavity, realizing the off-state of the modulator. The insertion loss is 0.07 dB, the extinction ratio is 22.5 dB, and the 3 dB bandwidth is about 100 GHz. The modulated incident light enters the mode division multiplexer. In the phase matching region, the effective index of the single-mode waveguide and the multi-mode waveguide is equal, and the TE₀ modes are converted into TE₁ modes and TE₂ modes. The insertion loss is less than 0.1 dB, and the channel crosstalk is less than -26 dB. The TE₀ modes input from the three ports are output from the same port in different modes.In conclusion, a three-channel integrated device for graphene electro-optic modulation and mode division multiplexing is proposed. The integrated device can realize modulation and mode division multiplexing of TE₀ modes, TE₁ modes, and TE₂ modes at the same time. The simulation results using the three-dimensional finite-difference time-domain method show that when the wavelength is 1 570 nm, the extinction ratio of the integrated device is greater than 28.3 dB, the insertion loss is less than 0.21 dB, the channel crosstalk is less than -28.6 dB, and the 3 dB bandwidth of the modulator reaches 100 GHz. The integrated device has excellent performance and has important application value in high-capacity optical communication systems.