A high-gradient radiofrequency (RF) gun oper-ated in continuous-wave (CW) mode is required in various accelerating applications. Due to the high RF power loss, a traditional normal-conducting (NC) RF electron gun has difficulty meeting the requirement of generating a high-repetition-rate electron beam. The development of a scheme for a CW NC-RF gun is urgently required. Demonstrated as a photoinjector of a high-repetition-rate free-electron laser (FEL), an electron gun operated in CW mode and the VHF band is designed. An analysis of the reentrant gun cavity is presented in this paper to increase the gradient and decrease the power density and power dissipation. Referring to the analysis results, the design of a 162.5 MHz gun cavity is optimized by a multi-objective evolutionary algorithm to achieve better performance in CW mode. Multipacting and thermal analyses are also deliberated in the design to coordinate with RF and mechanical design. The optimized 162.5 MHz gun cavity can be operated in CW mode to generate a high-repetition-rate beam with voltage up to 1 MV and gradient up to 32.75 MV/m at the cathode.