We developed a special combination of vortex method and particle trajectory tracking method, which is applicable to internal unsteady two-phase flows. This method is a completely grid-free Lagrangian-Lagrangian simulation, which is able to simulate interactions between particles and fluid flow. In this study, internal liquid-solid two-phase flows in a mixing tee had been analyzed by the new method, in which use of vortex introduction model enables us to simulate dynamic behaviors of separation or reattachment vortices. We simulated and measured particle motions, such as deposition or particle-wall collision, which change according to confluent flow rate ratio in a mixing tee. Calculation results showed good agreements with this experimental data. The present method can be useful in the design of industrial multiphase flows.