Abstract: The property of the lumped mass finite element method (LMFEM) on rectangular mesh is investigated to solve a typical parabolic problem, i.e., the heat transfer equation. The integral formula of the bi-linear finite element basis function on the rectangular mesh is given to discuss the error estimation for LMFEM. It is found that LMFEM has the equivalent approximate accuracy to the standard finite element method on the rectangular mesh, while the former has less computational cost and can retain the maximum principle under certain conditions. Moreover, the partitioning conditions for retaining the maximum principle on rectangular mesh are given.