This work has studied the influence of the generatrix's curvature of a dome-shaped patterned sapphire substrate (PSS) on the efficacy of GaN-based light emitting diodes (LEDs). The generatrix's central angle is carefully optimized by optical simulation. It is revealed that the dome-shaped PSS with a generatrix central angle of 10째 is optimal to improve the luminous efficacy of LED devices. Subsequent crystal growth and characterization of LED wafers grown on dome-shaped PSSs with different generatrix central angles indicate that the central angle will not influence the as-grown LED wafers' crystalline quality, and the optimal central angle of 10째 can enhance LED efficacy by about 19%.