The gain bandwidth of optical parametric chirped pulse amplification pumped by divergent beams has been theoretically studied. Several gain curves are simulated when the pump are non-diffraction-limited Gaussian beams or a beams having rectangular distribution in spatial spectrum respectively，using the method of Fourier transform and the fourth-order Runge-Kutta algorithm. The results show that the gain bandwidth of optical parametric chirped pulse amplification can be obviously improved by using divergent pump beams, either in the visible or in the near infrared region. Very high gain and broadband spectrum can be obtained if the divergence angle and intensity of the pump is selected properly.