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Lithium niobate on insulator (LNOI) is a promising platform for high-speed photonic integrated circuits (PICs) that are used for communication systems due to the excellent electro-optic properties of lithium niobate (LN). In such circuits, the high-speed electro-optical modulators and switches need to be integrated with passive circuit components that are used for routing the optical signals. Polarization beam splitters (PBSs) are one of the fundamental passive circuit components for high-speed PICs that can be used to (de)multiplex two orthogonal polarization optical modes, enabling on-chip polarization division multiplexing (PDM) systems, which are suitable for enhancing the data capacity of PICs. In this Letter, we design and experimentally demonstrate a high-performance PBS constructed by a photonic crystal (PC)-assisted multimode interference (MMI) coupler. The measured polarization extinction ratio (ER) of the fabricated device is 15 dB in the wavelength range from 1525 to 1565 nm, which makes them suitable for the high-speed and large data capacity PICs required for future communication systems.