Mode converter, achieving the mode conversion from fundamental mode to higher-order mode, is a key component for the on-chip multimode transmission and mode division multiplexing transmission. Here, a nanowire-loaded mode converter based on the thin film lithium niobate (TFLN) waveguide is proposed. The mode conversion structure is consisted of a nanowire grating and a phase change material based rectangular nanowire, where both of them are deposited atop the TFLN waveguide. Based on such structure, detailed structural analyses and optimizations are conducted, where the required conversion length is only 6μm and the central wavelength is 1.55μm for the mode conversion from input TE0 mode to output TE1 mode. The mode conversion efficiency, crosstalk, and insertion loss are 97.6%, -19.7dB, and 0.31dB, respectively. The device structure is further extended and the mode conversion is botained from input TE0 mode to output TE2 mode, TE3 mode and TE4 mode in the same length. If the device structure is obtained, other higher-order modes can also be obtained. The proposed device structure and scheme could benefit the multimode transmission for the TFLN waveguide and boost the development of photonic integrated components and circuits based on the TFLN platform.