In this Letter, we propose and demonstrate a fiber-to-chip edge coupler (EC) on an x-cut thin film lithium niobate (TFLN) for polarization-insensitive (PI) coupling. The EC consists of three width-tapered full-etched waveguides with silica cladding and matches well with a single-mode fiber (SMF). The measured results show that the minimum coupling losses for TE0/TM0 modes remain to be 0.9 dB/1.1 dB per facet, and the polarization dependent loss (PDL) is <0.5 dB over the wavelength range from 1260 to 1340 nm. Moreover, the EC features large misalignment tolerance of ±2 µm in the Z direction and ±1.5 µm in the X direction for both polarizations for a 1 dB penalty. To the best of our knowledge, this is the first realized O-band edge coupler on TFLN with SMF. The proposed device shows promising potential for integration into TFLN polarization diversity devices.