Starting from the four-wave maxing coupled equations, we obtain the optical field expression of a fiber optical parametric amplifier (FOPA) pulse source. Furthermore, we analyze the evolvement of pulse frequency chirp and amplitude when the signal light is phase or intensity modulated. It is concluded that the pulse width has no significant improvement but the extinction ratio is improved when the signal light is intensity modulated; however, when the signal light is phase modulated, the pulse has enhanced positive linear frequency chirp, which means that we may obtain shorter pulse than that of the FOPA based pulse source which has the same pump power but without phase modulation on signal light. Finally, theexperimental results of 10 GHz operation demonstrated the validity of our theoretical analysis. Using the FOPA pulse source with 05 W average pump power and phase modulated signal light, the transform limited pulse is obtained which has 22 dB extinction ratio and 52 ps pulse width, which is 2 ps narrower than that without modulation.