The　state　of　charge　(SOC)　plays　a　crucial　role　in　battery　management　system,　which　directly　reflects　the　usage　of　the　battery.　Recently　the　extreme　learning　machine　(ELM)　model　as　a　data-driven　method　has　been　utilized　to　estimate　SOC　due　to　its　simple　single　hidden　layer　structure　and　fast　learning　performance.　The　battery　management　system,　however,　may　usually　work　in　complex　working　conditions,　which　means　that　the　non-Gaussian　complex　noise　(or　outliers)　interference　problem　may　exist　in　some　measurement　data　for　model　training.　So　the　performance　of　the　classical　ELM　with　mean　square　error　(MSE)　criterion　may　be　degraded　under　this　case.　This　work　considers　Non-Gaussian　noise　interference　issue,　the　MSE　in　ELM　is　substituted　by　mixture　generalized　maximum　correntropy　criterion　(MGMCC),　and　a　novel　robust　ELM　model　is　developed　to　improve　the　SOC　estimation　capability　which　mainly　relies　on　the　stable　and　robust　nonlinear　similarity　characteristics　of　the　MGMCC.　A　data　set　from　a　Panasonic　18,650　battery　cell　is　used　to　verify　the　robustness　of　the　proposed　model,　the　experiment　results　demonstrate　that　it　can　achieve　better　estimation　performance　in　terms　of　different　evaluation　metrics　compared　with　the　traditional　methods.　©　2021　Elsevier　Ltd