Lithium　battery　is　a　reliable　source　for　mobile,　computers　and　electric　vehicles.　However,　the　internal　chemical　reaction　of　lithium　battery　is　complex　and　susceptible　to　external　influences,　such　that　the　traditional　model-driven　approach　cannot　model　it　accurately.　In　this　paper,　based　on　the　data-driven　approach,　an　expectation　maximization　algorithm　is　proposed　to　model　a　class　of　lithium　battery.　By　using　the　expectation　maximization　algorithm,　the　model　parameters　and　actual　values　of　test,　as　well　as　the　noise　intensity　can　be　identified　simultaneously.　The　NASA　battery　data　sets　are　employed　to　demonstrate　the　effectiveness　of　the　proposed　algorithm.　Several　indices　are　presented　to　evaluate　the　inferred　lithium　battery　models.　(C)　2015　Elsevier　B.V.　All　rights　reserved.