A finite element code is developed for the two-dimensional cure simulation of thick composite structures. In contrast to one or two-dimensional codes based on the finite difference method, the present finite element method can easily model composite structures with arbitrary shapes including the mandrel used for the cure set-up. For the two-dimensional cure simulation, a degeneration method to build the thermal conductivity matrix is proposed. The present finite element method is verified by two numerical examples. The numerical results show good agreement with the measured data appeared in the literatures. However, a full three-dimensional cure simulation is needed for more accurate cure simulation.