In this work, we propose and experimentally demonstrate a broadband polarization splitter-rotator (PSR) on the lithium niobate on insulator (LNOI). With multiple sequentially connected adiabatic tapers for waveguide mode conversion and directional coupling, the PSR shows a 160-nm bandwidth covering the C and L bands, an insertion loss of less than 2 dB, and an extinction ratio of more than 11 dB. Benefiting from the conversion-enhanced adiabatic tapers, the broadband device has a short length of 405 µm. Further optimization is performed to reduce the device length to 271 µm and comparable performances are achieved, demonstrating the feasibility of higher device compactness. The proposed design and principle can contribute to high-performance polarization management for integrated lithium niobate photonics.