The turbulent flow around a cavitating controllable pitch propeller (CPP) is simulated by solving the Reynolds-Averaged Navier-Stokes (RANS) equations, to investigate the dynamic effects on cavitation when the pitch of propeller blades is changed at different pitch adjustment velocities (PAVs). The process of changing the pitch at prescribed PAVs is controlled by a user-defined function (UDF) in the software FLUENT, and during the process, the time-dependent flow domain is re-discretized at each time step with dynamic meshes. The SST k-ω turbulence model and the cavitation model proposed by Schnerr and Sauer are employed in the simulation. The numerical simulation approach is first validated against model experiments for a fixed pitch propeller (FPP) working in the open water. A grid dependence study is carried out to determine a proper mesh resolution for the simulation of such cavitating flows; then the hydrodynamic performance as well as the extent and volume of the sheet cavities obtained from the RANS simulations are compared with experimental data. Then influences of the PAV on the hydrodynamic performance and cavity geometry are investigated. The CPP blades are rotated around the spindle axes to change the pitch, and the movement is controlled by a UDF. The PAV is prescribed and kept constant in the process of adjusting the pitch. At different PAVs, the unsteady thrust and torque, pressure distributions on blade surfaces and propeller disk, cavity geometry, as well as cavitation volume of the cavitating flow are compared with each other to assess the dynamic effects of the PAV.