This paper presents the concept of a Dielectric-lined Multiwave Cerenkov Generator (DMWCG), which is investigated with particle simulation method. It is showed that the DMWCG can operate in a lower diode-voltage range with much higher radiation efficiency as compared with the usual Multiwave Cerenkov Generator(MWCG). This result shows a possible way for the application of the DMWCG into such a field as high power microwave generation with Explosive Magnetic Compression. Also showed through the simulation are both the downshift of the microwave frequency in the presence of the liner and the existence of the optima for the permittivity of the liner as well as for the magnitude of the guiding magnetic field.