Abstract: A combined approach of the precise integration boundary element method and the front-tracking method is presented for thermal conduction problems with one-phase solidification. Firstly, the boundary integral equation of transient thermal conduction is given by using the fundamental solution of steady-state thermal conduction problems and radial integration method. The precise integration method is applied to solve the discrete differential equations for obtaining the heat flux density of the moving boundary. Then the energy conservation equation of the moving boundary and the front-tracking method are applied to predict the position of the moving boundary, and the results of numerical simulations are obtained. To validate the proposed method, two typical examples are given and compared with the analytical solutions. The results show that the proposed method has a high accuracy and is an effective numerical method for solving thermal conduction problems with phase solidification.