A new control volume based enthalpy method is described here that is designed to solve inverse phase change problems. The new method uses a direct solution procedure which is simpler, efficient, and more stable than the iterative methods found in the literature. Several 1D test problems are considered to illustrate the proposed method, including 1D freezing problems with constant and variable phase front velocities. The effect of the Fully Implicit and Crank-Nicolson numerical schemes on these solutions is examined. Results obtained from these computations are compared with both the old numerical solutions and the exact solutions. The agreement between the current numerical solution and the exact solution is found excellent.