Abstract: This paper proposed a numerical scheme to simulate the hydraulic fracture propagation in a frame by an extended finite element method, in which a crack representation is explicit and independent of the mesh grid. The crack faces are treated as internal boundaries, which are opened and supported by hydraulic pressure. An integral scheme is presented to an equal the hydraulic pressure as nodal forces. The interactive integral method is used to calculate the stress intensity factor with the consideration of hydraulic pressure on crack faces. The maximum energy release criterion is selected to determine the propagation condition and crack direction. The corresponding code was prepared and used to simulate the non-planar propagation of a single hydraulic fracture with a constant hydraulic pressure. The numerical results are compared with the lab test and the analytical model. The results show that the numerical results of mode I have an excellent agreement with analytical results, in which the maximum relative error is below 0.45%.