Ultraviolet random lasing from ZnO and Mg(0.1)Zn(0.9)O films have been achieved under optical pump of a continuous wave He-Cd laser as the films are simultaneously exerted by an electric-field with appropriate polarity and amplitude. With the aid of electric-field, the optical pump intensity for generating random lasing can be reduced at least five orders of magnitude in comparison with conventional pulse-laser pumped ones. It is believed that the role of electric-field exerted on the films is similar to that of increasing optical pump intensity, in terms of increasing the amount of non-equilibrium electrons in the near-surface regions of films.