Liquid nitrogen fracturing granite is a complex multi-field coupling process including conjugate heat transfer between fluid and rock, nonlinear deformation and damage of rock. Especially for high temperature rock, the tremendous temperature difference between flow and rock forces us not to simply ignore the thermal stress. Investigating the law of heat transfer and stress between fluid and rock during liquid nitrogen cycle can help us to understand the variation characteristics of temperature and stress field of rock more intuitively, and help to reveal the mechanism of crack initiation and propagation of liquid nitrogen fracturing. In this paper, based on the finite element method, a heat transfer-stress coupling model before the initiation of liquid nitrogen fracturing cracks is established. The effects of temperature, heat flux density and cycle time on rock temperature and stress are compared and analyzed. The influence of liquid nitrogen ultra-low temperature impact on rock temperature and stress field is obtained, and the mechanism of thermal stress assisted rock failure is revealed. According to results, the heat transfer rate between liquid nitrogen and granite is slow and the changes of temperature and stress field are mainly concentrated near the bottom of well. With the increase of initial temperature of the granite, heat transfer time and heat flux, the thermal impact of LN2 increases greatly and the fracturing results become better. The research results preliminarily reveal the initiation and propagation mechanism of granite under liquid nitrogen fracturing, which is expected to provide some theoretical basis for forming a new liquid nitrogen fracturing technology in deep hot dry rocks reservoirs.