Based on the critical damage principle, a new prediction model for fatigue crack initiation life (FCIL) is developed through taking the cyclic damage strain range as the damage parameter. Correlations between the monotonic tensile data and two of the material constants (the stress fatigue-resisting coefficient and the theoretical fatigue threshold) in the proposed FCIL prediction model are founded as well. In contrast to Zheng's model, the fatigue ductility exponent contained in the proposed FCIL prediction model is a material constant which doesn't identically equal to the constant value -0.5. Besides, the fatigue ductility exponent shows the damage resistance ability of the material. The expressions of fatigue life curves with given survivability (PSN curves) for 45 steel notched specimen are developed on the basis of the proposed FCIL predication model. In comparison with the Zheng's model-based PSN curves, the new PSN curves can be used to predict the fatigue life with given survivability of 45 steel better.