A　domain　map　fmite　element　method　was　applied　to　the　three　dimensional　(3-D)　numerical　mode-matching　(NMM)　method　to　solve　the　3-D　electric　logging　problem.　This　method　divides　the　infinite　field　domain　of　every　layer　into　inner　and　outer　field　domains,　in　inner　domain　the　matrices　are　formed　by　standard　FEM　and　in　outer　domain,　the　Kelvin　transformation　is　applied　and　the　matrices　are　formed　by　a　new　infinite　element　format.　Matrices　of　two　different　parts　are　coupled　in　the　domains＇　common　interface　to　form　the　final　matrices　of　the　original　problem.　This　method　generates　smaller　size　of　generalized　matrices　than　original　3-DNMM　method.　In　addition,　this　method　changes　the　distribution　of　eigenvalues　which　needs　less　eigenvalues　under　the　same　error.　Results　show　that　the　new　method　spends　only　1/7　CPU　time　and　uses　only　1/3　memory　of　the　original　method.