Based on an integrated silicon platform, a device for generating and multiplexing optical orbital angular momentum modes is proposed, which is consisted of asymmetric directional coupler and trench waveguides. According to the principle of phase matching, the fundamental mode TE₀₀ is coupled to the first-order mode via an asymmetric directional coupler. Single-trench waveguide can support two orthogonal linear polarization-like modes whose optical axes are rotated by around 45° with respect to the horizontal and vertical directions. Adjusting the phase difference of two orthogonal eigenmodes to make them degenerate, TE₀₀ can be converted into orbital angular momentum modes with various topological charges, and multiplexed in the second trench. The simulation is carried out with finite difference domain method. The results show that the device can realize the generation and multiplex of orbital angular momentum modes with topological charges of +1, 0, -1. The proposed device is very compact with a footprint of < 80 μm×5.3 μm and an insertion loss of 0.24 dB, and is fit for a wavelength range from 1.47 μm to 1.58 μm. The structure is simple and easy to integrate, having a good application in orbital angular momentum multiplexing system.