Maximum expansion angle is the primary parameter for the design of expansion section of hypersonic quiet nozzle. According to the quantity of maximum expansion angle, expansion section could be classified as fast expansion and slow expansion. In order to diminish the effect of instability of Görtler vortex, gradually, slow expansion was employed for quiet nozzle design. Based on the favorable pressure effect, the maximum expansion angle is optimized in this paper, and a considerable selective session of maximum expansion angle is obtained. The trend that slow expansion is employed instead of fast expansion is explained, and a new method is established for aerodynamic optimization of expansion section contour in a quiet nozzle.