Abstract: On the basis of prediction of the moving boundary the adaptive implementation of mesh for distributed parameter systems (DPS) with moving boundary is put forward in this paper. Then the numerical performance of DPS with moving boundary is obtained by the application of the finite-element approach to the enthalpy formulation. This method may be used to overcome the contradiction of numerical ac- curacy near the moving boundary with the heavy computation burden which results from dense meshes. Moreover, this method is useful in the modelling and simulation of DPS with moving boundary and provide a valid means for the study of the control and estimation of this kind of systems.