The cavitation of a push-type ducted azimuth propulsor with the design target of balancing the large thrust under bollard condition and the required speed is numerically simulated under the maximum speed condition and the bollard conditions by using the Reynolds-Averaged Navier-Stokes (RANS) method with the SST k-ω model and Schnerr-Sauer cavitation model. The calculated cavitation pattern is generally in accordance with the experimental results. It captures the sheet cavitation on the back blade, the blade face cavitation, the tip-vortex cavitation and the tip-leakage cavitation. The propeller-hull vortex (PHV) cavitation is observed due to the close distance between the strut and the duct and ducted propeller. The correlation between the distance of the strut and the ducted propeller and the strength of the PHV is then analyzed to propose the distance that can suppress the generation of the PHV. The distance which is greater than 0.35D can basically eliminate the PHV. It provides an important support for the optimization design of the ducted azimuth propulsor based on the cavitation performance.