A floating horizontal-axis tidal current turbine (HATT) is an underwater power generation device where cavitation inevitably occurs on blade surfaces, severely affecting a turbine's lifespan. Under wave action, these floating turbines exhibit six degrees of freedom motion, potentially intensifying the cavitation on the blade surfaces. This study selects three types of oscillatory motions from the six degrees of freedom: roll, yaw, and pitch. Computational fluid dynamics (CFD) methods are used for numerical calculations, and transient simulations of multiphase flow are conducted on the basis of the Reynolds-Averaged Navier-Stokes (RANS) model. Research has revealed strong correlations between flow velocity, the blade tip speed ratio, and cavitation. During oscillatory motion, the motion period and amplitude also significantly impact cavitation. In roll motion, the cavitation rate can increase by up to 59% with decreasing period, whereas in pitch and yaw motions, the increases are 7.57 times and 36% larger, respectively. With an increase in amplitude during roll motion, the cavitation rate can increase by up to 1.08 times, whereas in pitch and yaw motions, the increases are 3.49 times and 45%, respectively. The cavitation rate on the blade surfaces is the highest in pitch motion, followed by roll and yaw motions.