A coaxial reflex triode oscillator for high power microwave generation is proposed and studied by numerical simulation. In the proposed oscillator, a small cylindrical conductor is added on the cathode along the centreline. Thus electric gradient is formed in the interaction region. This is benefical to the reflection of electrons between the real and virtual cathode. For an electron beam of 590 kV and 19.1 kA, by optimizing of structure parameters, the efficiency can reach 15% at an output power of 1.7 GW at 3.62 GHz. Preliminary analysis of the physical mechanism shows that microwave generation comes mainly from the oscillations of the reflex electrons.