A pressure-based algorithm for the prediction of cavitating flows is presented. The algorithm employs a set of equations including the Navier-Stokes equations and a cavitation model explaining the phase change between liquid and vapor. A pressure-based method is used to construct the algorithm and the coupling between pressure and velocity is considered. The pressure correction equation is derived from a new continuity equation which employs a source term related to phase change rate instead of the material derivative of density Dp/Dt. This pressure-based algorithm allows for the computation of steady or unsteady, 2-D or 3-D cavitating flows. Two 2-D cases, flows around a flat-nose cylinder and around a NACA0015 hydrofoil, are simulated respectively, and the periodic cavitation behaviors associated with the re-entrant jets are captured. This algorithm shows good capability of computating time-dependent cavitating flows.