Quantum-well semiconductor optical amplifiers (QW-SOAs) have been widely used in all-optical signal processing functions because of their various nonlinear effects. For different optical signal processing functions, the requirements for performance of the QW-SOAs are different, and nonlinear effects of the QW-SOAs should be controlled selectively. Engineering nonlinear effects of QW-SOA is very important for different applications in optical signal processing. Here, a comprehensive QW-SOA model by combining the QW band structure calculation with the dynamic model is established to connect the structure parameters with the nonlinear effects of QW-SOA. Those characterized parameters of the QW-SOAs, such as gain coefficient, differential gain coefficient, refractive index change, differential refractive index change, linewidth enhancement factor, third-order susceptibility and polarization dependent gain, are used to characterize the nonlinear effects, and are calculated with different structure parameters based on this developed model. Take the wavelength conversion based on cross gain modulation effect and four wave mixing effect as examples, the structure parameters of the QW-SOAs are optimized for engineering the nonlinear effects and achieving the best output performance. This theoretical work presents a guide for choosing the optimized structure parameters while fabricating the QW-SOAs for different optical signal processing functions