Lithium niobate on insulator (LNOI) is a promising platform for photonic integrated circuits (PICs), and 3-dB power splitters are the most essential building blocks in PICs. In this Letter, we propose and demonstrate a broadband, fabrication-tolerant 3-dB power splitter based on the photonic bound state in the continuum (BIC) and using a spatial adiabatic passage structure on a polymer-loaded LNOI platform. The simulation results show that the proposed device can achieve a splitting ratio of 50%:50% with an excellent operating bandwidth of 180 nm (from 1450 nm to 1630 nm). The fabricated device on the EpoCore-loaded LNOI platform features a power-splitting ratio of ∼50.13%:49.87% for both output ports within the 1530-1630 nm wavelength range. With its outstanding performance and simple fabrication process, the demonstrated 3-dB power splitter is essential for on-chip optical interconnect systems.