This paper proposes a method for generating an ultraviolet supercontinuum light source (SC) using highly nonlinear magnesium fluoride photonic crystal fiber (PCF). The nonlinear Schr?dinger equation was solved using the split-step Fourier method, and the generation of an ultraviolet SC in the PCF was numerically simulated. The effects of the structural parameters of the PCF and the parameters of the pump source on the ultraviolet SC were analyzed. The variations in the SC width relative to the PCF length, dispersion parameter, pump pulse peak power, and initial width of pump pulses were obtained. Simulation results reveal that the SC is extended into the ultraviolet range of 279.6--769.0 nm when the length of the PCF is 8 cm, central wavelength of the pump pulse is 450 nm, peak power is 3.1 kW, and initial pulse width is 40 fs.