The phase-matching configuration of optical parametric amplification (OPA) is investigated. The general physical model for evaluating the phase-matching scheme capable of generating ultra-broad gain bandwidth is developed. Based on this model, the phase-matching configuration and the corresponding matching signal wavelength can be obtained only under the conditions of a given pump wavelength and nonlinear crystal parameters. Numerical simulations, taking β-BaB2O4 (BBO) crystal for example, are performed, and the results show that there is a extreme difference for the acceptance angles between two different non-collinear phase-matching configurations. Analysis and optimization of non-collinear phase matching parameters are also carried out in order to obtain maximum gain bandwidth and excellent crystal acceptance angle. The calculated results of spectral phase-matching range for OPA based on BBO crystal, can also provide a theoretical basis for the designs of multi-beam-pumped or multi-stage OPA systems.