According to the coupled mode theory, a three-core fiber based three-mode multiplexer/demultiplexer supporting to transmit three spatial modes (LP01, LP11a, LP11b) is designed. This three-core fiber consists of a three-mode core located in the center and two single-mode cores deployed in the outer layer. The structural parameters of the three-mode core are chosen, and then according to the effective refractive index matching principle of mode, parameters of two single-mode cores in the outer layer are designed. The power conversion processes between LP11a mode and LP01 mode, as well as LP11b mode and LP01 mode, are analyzed by simulation, respectively. The optimal fiber length obtained is 5.2 mm. Finally, in C+L band, the working bandwidth provided by the three-mode multiplexer/demultiplexer is 50 nm for mode conversion efficiency of 90%. This three-core fiber based three-mode multiplexer/demultiplexer has plenty of advantages, such as simple structure, high mode conversion efficiency, small splice loss, and wide band.