Mode (de)multiplexers (MDMs) serve as critical foundational elements within systems for facilitating high-capacity communication, relying on mode conversions achieved through directional coupler (DC) structures. However, DC structures are challenged by dispersion issues for broadband mode coupling, particularly for high-order modes. In this work, based on the principles of phase control theory, we have devised an approach to mitigate the dispersion challenges, focusing on a thin-film lithium niobate-on-onsulator (LNOI) platform. This solution involves integrating a customized inverse-dispersion section into the device architecture, offsetting minor phase shifts encountered during the mode coupling process. By employing this approach, we have achieved broadband mode conversion from TE0 to TE1 and TE0 to TE2 within a 300 nm wavelength range, and the maximum deviations were maintained below −0.68 dB and −0.78 dB, respectively. Furthermore, the device exhibited remarkably low crosstalk, reaching down to −26 dB.