An implicit enthalpy solution is developed for analysis of one-dimensional conduction controlled phase change problems. The solution is based on separating the sensible and latent heat terms in an enthalpy formulation. By making the assumption of equal volume node-jumping,a variable time together with a fixed space grid is used to ensure that the phase boundary is always on a node point,so that the nonlinearity associated with the latent heat can be effectively dealt with via the source term. A freezing problem around a pipe with analytical solution is applied to demonstrate the effect of the present method.