The spectral properties of broadband pumped optical parametric amplification (BPOPA) are investigated theoretically. General mathematical expression to describe the relationship between the pump bandwidth (BW) and the parametric BW is achieved. There exist broaden and compression point of parametric spectral BW by observing the figures origin from obtained expression. Results obtained show good accordance with published experiments and the numerical simulations, which is calculated by means of three-wave mixing equations. The results are helpful for optimization of broadband pump-based OPA and optical parametric oscillation.