Thin film lithium niobate (TFLN) has become an platform for modern integrated circuits due to its excellent optical properties. With the development of rare earth ion doped TFLN, important breakthroughs of on-chip microlasers has emerged and show significant application for optical communication, computing and quantum photonics. However, challenges still remain in developing compact lasers with small mode volumes and low threshold on rare earth ion doped TFLN for highly efficient dense integration. In this letter, we fabricated a heterogeneous photonic crystal (PhC) nanobeam cavity on erbium-doped TFLN with a quality factor of 1.2\times10^4 and firstly demonstrated a single-mode integrated PhC laser with submicron mode volume on TFLN platform. Laser at 1559.63 nm is achieved with the 974 nm single-mode pump. The effective mode volume is 1.44 ({\lambda}/n)^3 (~ 0.645 {\mu}m^3) and the threshold power is 163 {\mu}W. Enhanced photorefractive effect in the PhC cavity is measured. This lithium niobate photonic crystal nanocavity laser, as a compact telecommunication C-band on-chip light source, would benefit the progress of high-speed and low-cost optical community on TFLN integrated photonics.
