Based on the dynamics of rolling bearing,an improved slice method is used to solve the problem of needle-race contact,and the dynamics differential equations are established and solved by Predicting-Correcting GSTIFF（ Gear Stiff） integer algorithm with variable step. The impact of working parameters and roller crowned shape on the stress distribution of needle-race and bearing life is investigated theoretically,and it shows that,working conditions of bearing and roller crowned shape both have large effect on the fatigue life of bearing. Therefore,the optimum crowned shape of roller should be determined according to the working conditions of bearing.