The klystron-like relativistic backward wave oscillator (RBWO) combines the transition radiation with Cerenkov radiation and has demonstrated microwave output of high power and high efficiency. The coaxial slow wave structure device can produce microwave with a lower frequency in a smaller cross section. For the purpose of high efficiency, low frequency, and miniaturization, a coaxial klystron-like RBWO with a premodulation cavity is presented. Particle-in-cell simulations show that a microwave with power of 1.15 GW and frequency of 2.1 GHz is generated with conversion efficiency of 48%, whereas for the device with a reflector, the efficiency is 38%.