We proposed a three-dimensional model to simulate terahertz generation from LiNbO3 crystal under intense laser excition (up to ~50 mJ/cm2). The impact of three-photon absorption, which leads to free carrier generation and free carrier saturation (when pump fluence above ~10 mJ/cm2) on terahertz generation was investigated. And further with this model, we stated the optimized experimental conditions (incident postion, beam diameter, and pulse duration, etc) for maximum generation efficiency in commonly-used tilted-pulse-front scheme. Red shift of spectrum, spatial distribution "splitting" effects of emitted THz beam, and primilary experimental verification under intense laser excitation are given.