In research on hybrid quantum networks, visible or near-infrared frequency conversion has been realized. However, technical limitations mean that there have been few studies involving the ultraviolet band, and unfortunately the wavelengths of the rare-earth or alkaline-earth metal atoms or ions that are used widely in research on quantum information are often in the UV band. Therefore, frequency conversion of the ultraviolet band is very important. In this paper, we demonstrate a quantum frequency conversion between ultraviolet and visible wavelengths by fabricating waveguides in a period-poled MgO:LiTaO3 crystal with a laser writing system, which will be used to connect the wavelength of the dipole transition of 171Yb+ at 369.5 nm and the absorption wavelength of Eu3+ at 580 nm in a solid-state quantum memory system. An external conversion efficiency of 0.85% and a signal-to-noise ratio of greater than 500 are realized with a pumping power of 3.28 W at 1018 nm. Furthermore, we complete frequency conversion of the classical polarization state by means of a symmetric optical setup based on the fabricated waveguide, and the process fidelity of the conversion is (96.13 ± 0.021)%. This converter paves the way for constructing a hybrid quantum network and realizing a quantum router in the ultraviolet band in the future.