We investigate the parametric amplification and its saturation characteristics in a directly modulated semiconductor laser. The parametric gain depends on the resonance frequency shift that occurs due to the pump modulation current and the bias current. Also, the parametric gain is a strong function of the phase between the signal and the pump modulation currents. The saturation characteristic of the parametric amplification occurs at a large signal modulation current due to depletion of the pump by an amplified optical signal. We explain the observed behaviors using the analytic results of the nonlinear rate equations of the semiconductor laser.