The analysis took two points into account, namely quadratic characters of plastic strain amplitude vs. reversals to failure in log-log scale coordinates and the residual stabilization. Based on power transformation methods, it advanced a power-exponent function model for LCF(low cycle fatigue) life prediction. The investigation gave some power transformation exponents (p) and model performances contrast results of some materials. The contrast results show that power-exponent function model has better performances and precisions for LCF life prediction. In fact, Manson-Coffin equation is the first order Taylor expansion approximation of power-exponent function model in log-log scale coordinates and is the equivalence form when p is equal to 1. The enhancement of nonlinearity makes the power-exponent function model have better precision. The new life prediction model remains the simpleness for engineering application so that the model parameter estimation still uses linear regression method.