The free-surface flows with particles are widely found in chemical engineering, and numerical modeling is a strong computing tool for in-depth understanding of the local and macrocharacteristics. In this study, a discrete element method volume-of-fluid (DEM-VOF) model is extended to turbulent free-surface flows with particles, by means of Reynolds stress model. Also, we adopt a novel virtual dual grid porosity model to calculate the fluid porosity. The simulated results of single particle sedimentation, the falling of sinking particles, and the floating of buoyant particles agree well to analytical and literatures, which validate the proposed DEM-VOF model. Furthermore, the DEM-VOF model developed in this paper is applied to the simulation of free surface flow with particles in solid-liquid mixing system for the first time. It is found that elliptical-head vessel is preferred to a flat-bottomed vessel for solid-liquid mixing by comparing the simulation results of four different stirred tanks, which agrees well to the related content of the book Handbook of Industrial Mixing (Paul, E. L.; Atiemo-Obeng, V. A.; Kresta, S. M. Eds.; John Wiley & Sons, 2004).