Using　the　base　forces　as　fundamental　variables　to　describe　the　stress　state　and　the　displacement　gradients　that　are　the　conjugate　variables　of　the　base　forces　to　describe　the　deformation　state　for　the　two-dimensional　elasticity　problems,　a　4-mid-node　plane　model　of　base　force　element　method　(BFEM)　based　on　complementary　energy　principle　is　proposed.　In　this　paper,　the　complementary　energy　of　an　element　of　the　BFEM　is　constructed　by　using　the　base　forces.　The　equilibrium　conditions　are　released　by　the　Lagrange　multiplier　method,　and　a　modified　complementary　energy　principle　described　by　the　base　forces　is　obtained.　The　formulation　of　the　4-mid-node　plane　element　of　the　BFEM　is　derived　by　assuming　that　the　stress　is　uniformly　distributed　on　each　edge　of　the　plane　elements.　A　procedure　of　the　BFEM　on　complementary　energy　principle　is　developed　using　MATLAB　language.　The　numerical　results　of　examples　show　that　this　model　of　the　BFEM　has　high　precision　and　is　free　from　mesh　sensitivity.　This　model　shows　good　performances.