Frequency doubling in an external cavity is a prevalent method to generate an ultra- violet laser at 397.5 nm . A semi-monolithic resonant frequency doubling cavity based on the PPKTP crystal is built and is used to realize the resonant frequency doubling of the 795 nm single frequency continuous-wave laser amplified via a semiconductor tapered amplifier. Under the condition of 203 mW input power of a 795 nm laser, the 397.5 nm single frequency continuous-wave ultra-violet laser with a power of 60.4 mW is obtained, and the frequency doubling conversion efficiency is 30%; and the maximum doubling efficiency is 34.6% with a fundamental power of about 87.5 mW. The beam quality factor M2 of the frequency doubling ultra-violet laser is superior to 1.21, indicating the better beam quality. The typical root-mean-square fluctuation of the output power within 30 min is less than 1.9%. This frequency doubler is compact, has good mechanical stability, and can be used to achieve steady output of ultraviolet laser. The ultra- violet laser can be used to generate the squeezed or entangled states of the rubidium transitionline, and plays an important role in the quantum optics, precise measurement and other fields.