A broadband mode-division multiplexer based on asymmetric three-core photonic crystal fiber is proposed in this paper. The device is mainly composed of a central core, which can provide the transmission of fundamental mode and higher-order mode, and two side cores providing fundamental mode transmission. According to the theory of optical coupling, the LP₀₁ mode light is input to the three fiber cores at the initial port separately, and in the transmission process the LP₀₁ mode on the left side core will be coupled and converted into the LP₂₁ mode light in the central core gradually. Similarly, the LP₀₁ mode of the right side core is transformed into the LP₃₁ mode of the center core. By optimizing the structural design and selecting the length of optical fiber, the best conversion from side core into central core can be completed at the output end simultaneously, thereby realizing the multiplexing of LP₀₁, LP₂₁ and LP₃₁ modes in the central core. In the opposite direction, if the output end of the device is used as the initial port, the demultiplexing of three modes of light from the central core to the three cores can be realized. In thiswork, the finite element method and beam propagation method are used to optimize the simulation, and the optical coupling theory and supermode theory are combined to conduct analysis and calculation. The results show that at wavelength band from 1.49 μm to 1.63 μm, the maximum insertion loss of the device is 0.72 dB, and the lowest insertion loss is 0.543 dB at 1.55 μm, which is far lower than the general evaluation standard of 1 dB insertion loss. The low insertion loss also makes it possible to design cascaded multi-core photonic-crystal-fiber mode-division multiplexer. Compared with the existing mode-division multiplexing scheme, the device is more integrated and less affected by the external environment. When it is used with multi-core space division multiplexing fiber, it can better improve the mode-conversion efficiency and mode purity, reduce the coupling complexity and expand the communication capacity.