A polarization splitter-rotator device can facilitate on-chip polarization-division multiplexing to enhance the transmission data rate. Here, we propose and experimentally demonstrate a polarization splitter-rotator based on adiabatic mode evolution on the thin-film lithium niobate platform. The measured results for a fabricated device show low insertion losses of <-0.5 dB and large extinction ratios of >20 dB over the 110-nm band. Large fabrication tolerance is also demonstrated with extinction ratios of >15 dB in the wavelength range of 1465-1630 nm for a waveguide width variation of 80 nm.