The electrically pumped ultraviolet (UV) random lasing and carrier transport of ZnO-based metal-insulator-semiconductor (MIS) structures on Si substrates have been systematically investigated. With the increase of positive bias voltage on the gates of the MIS devices, the current-voltage (I-V) characteristics manifest a normal curved I-V region where the current increases with the bias, followed by a negative differential resistance (NDR) region. Moreover, the UV electroluminescence from the devices in the normal region is transformed from spontaneous emission into increasingly intensive random lasing; while, that in the NDR region is transformed from random lasing into very weak spontaneous emission. The reason for the effect of NDR on the random lasing from the devices has been tentatively explored.