Modified parametric coupled equations for three-wave interaction in non-collinear optical parametric chirped-pulse amplification (OPCPA) are presented, in which the effects from the non-collinear configuration have been taken into account. By utilizing this new model, a two-stage OPCPA system based on a BBO crystal is numerically calculated with a split-step Fourier transform algorithm. Tracing the dynamics of the signal wave in the crystal reveals that in the first stage spectral gain narrowing occurs due to the weak input signal intensity and the non-uniform temporal distribution of the pump light. However, in the saturation regime the spectrum of the signal will be broadened as a consequence of back conversion. The simulation shows that it is crucial to correctly control the experimental parameters to balance both processes. For maximizing the energy-bandwidth product (EBP), an optimized configuration is sought by examining several parameters such as pump intensity, seed energy and crystal length. With a pump intensity of 7.75 GW/cm2 and a crystal length between 3.75 and 4.25 mm pulses with a sub-10 fs duration can be amplified with a total gain of up to 1.7×106.