Photonic crystal (PhC) cavities with high Q factor and low volume have been applied in nonlinear, electro-optic and acoustic-optic devices due to the enhancement of the light-matter interactions. However, there are few devices and research on LiNbO3 (LN) PhC cavities due to the difficulty in making hyperfine structures on LN platform. In this work, we propose a PhC nanobeam cavity on the etchless x-cut LiNbO3-On-Insulator (LNOI). The fabrication-friendly device has been designed based on photonic bound states in the continuum (BICs) exhibiting a high Q factor of over 10,000 with the device length of only about 100 µm. Utilizing the electro-optical effect γ13 of LN, we demonstrate an ultra-compact electro-optic modulator based on the PhC nanobeam cavities, which has the modulation efficiency of 1.5 pm/V and the 3 dB bandwidth of 28 GHz.