The　finite　element　method　based　on　the　complementary　energy　principle　and　its　combination　with　artificial　neural　networks　is　a　worthwhile　research　topic.　A　new　Base　Force　Element　Method　(BFEM)　model　is　proposed　in　this　study,　which　can　solve　the　problems　of　large　elastic　deformation　and　finite　strain　in　incompressible　hyperelastic　materials.　The　complementary　energy　function　of　nonlinear　elasticity　has　not　yet　been　proposed.　The　complementary　energy　function　is　replaced　by　a　pre-trained　Back-Propagation　(BP)　neural　network　to　establish　the　constitutive　relationship.　This　makes　it　easy　for　finite　strain　problems　to　be　studied　by　the　BFEM　model.　When　the　constitutive　relationships　of　different　incompressible　hyperelastic　materials　were　described,　only　two　parameters　needed　to　be　changed.　The　governing　equations　of　the　BFEM　model　are　general　and　concise,　and　its　derivation　process　does　not　involve　an　approximate　representation　of　shape　functions.　The　calculation　results　of　the　examples　indicate　that　the　model　has　high　accuracy.　This　new　numerical　method　fills　the　gap　in　using　the　complementary　energy　finite　element　method　to　calculate　the　finite　strain　problem　of　incompressible　hyperelastic　materials.