A comprehensive method is proposed to investigate gain narrowing and the gain saturation effect in a fiber chirped pulse amplification system. It can solve the comprehensive gain effect in time and spectral domains simultaneously based on the nonlinear Schrödinger equation. Through numerical simulation under various pump powers, our simulation results benefit from good agreement in principle with the corresponding experimental results. Our model enjoys ameliorated accuracy and generalized compatibility compared to some conventional models, thus paving the way for further applications in chirped pulse amplifications.