A novel Lagrangian algebraic slip mixture model (LASMM) has been developed to study multiphase flows. In this model, the slip velocity between continual and dispersed phases was developed through the bubble Lagrangian movement equation. According to the Lagrangian equation, the various interfacial forces at interface of the continual and dispersed phases were considered. Through the connection of the slip velocity, the Lagrangian equation was induced into the governing Eulerian equations of the two-phase mixture flow. This model therefore realized the connection between Eulerian model and Lagrangian model. Through the comparisons of the numerical simulations to the experiments in horizontal pipe, this model was validated. (C) 2013 Elsevier Ltd. All rights reserved.