The　accurate　and　real-time　estimation　of　state-of-charge　(SOC)　in　lithium-ion　batteries　(LIBs)　are　crucial　for　battery　management　system　(BMS)　in　electric　vehicles.　The　SOC　estimation　is　affected　by　several　factors　like　temperature,　aging　and　many　other　battery　characteristics,　making　it　challenging.　In　this　study,　improved　central　difference　transform　Kalman　filter　method　based　on　square　root　second-order　central　difference　transform　(SRCDKF)　was　utilized　for　real-time　estimation　of　SOC　in　LIBs.　The　hybrid　pulse　power　characterization　(HPPC)　tests　were　combined　with　recursive　least　squares　(RLS)　method　to　identify　the　second-order　equivalent　circuit　model　parameters.　To　avoid　high　order　Taylor　series　expansion　and　complicated　multi-parameter　adjustment　in　other　Kalman　filters,　the　CDKF　with　square　root　second-order　difference　transform　is　developed　to　generate　Sigma　point.　The　effectiveness　of　the　proposed　SRCDKF　was　then　verified　by　pulse　discharge　and　urban　dynamometer　driving　schedule　(UDDS)　testing,　and　the　results　were　compared　with　those　obtained　from　extended　Kalman　filter　(EKF)　and　unscented　Kalman　filter　(UKF).　In　particular,　the　proposed　algorithm　provided　small　error　within　2%　under　UDDS　testing,　and　the　convergence　time　was　earlier　than　those　obtained　with　the　other　two　algorithms.　The　proposed　SRCDKF　can　also　guarantee　the　non-negative　covariance　and　reduce　the　computational　complexity.　Overall,　these　findings　look　promising　for　future　BMS　SOC　estimation　in　practice.　©　2019　Elsevier　Ltd