A pressure correction method is developed to simulate fluid-particle interaction flows. In this Paper, the three-dimensional solid-fluid mixture flows are investigated. The pressure corrected method coupled with the direct-forcing immersed boundary (IB) and the volume of fluid (VOF) methods is used to simulate the mixture flows. A discrete element method (DEM) together with a multi-time-step algorithm is introduced into the pressure correction method to calculate the forces and torques between solid bodies and between solid bodies and walls. As a demonstration of the efficient and capabilities of the present method, four test cases are simulated. They include sedimentation of one spherical particle in an enclosure, collapse of six solid-cylinder layers, two-dimensional solid-fluid mixture flow, and three-dimensional solid-fluid mixture flow.