A Ku-band relativistic magnetron (RM) is designed in this paper to broaden working frequency range of this type of HPM source. An anode structure with 20 cavities is applied in this tube and the high frequency simulation results reveals that its π mode frequency is about 13.5 GHz. A Particle- in-Cell (PIC) simulation has been carried out with the all-cavity-axial-extraction (ACAE) structure. The high power microwave with power of 38 MW was detected at 13.47 GHz with power conversion efficiency of about 61.6% when the applied voltage was 150 kV, the current was 0.41 kA, and the inducing magnetic field was about 0.4 T. The simulation results reveal that the presented tube has a high conversion efficiency and a compact structure which brings a potential of light weight package with permanent magnet.