Purpose:　As　for　the　reliability　analysis　of　complex　engineer　problems,　the　nonlinearity　and　implicitness　of　the　limit　state　functions　always　stand　in　the　way.　On　one　hand,　the　nonlinearity　influences　the　convergence　computation　of　some　reliability　problems　when　using　most　methods　of　reliability　analysis.　On　the　other　hand,　the　implicitness　means　that　information　of　the　partial　derivatives　of　the　limit　state　function　is　impossible　to　obtain,　which　is　necessary　for　most　of　the　reliability　methods.　In　order　to　overcome　these　difficulties,　the　paper　presents　a　new　general　most　probable　point　based　(MPP-based)　approach　for　computing　the　reliability.　Methodology:　Within　the　framework　of　the　proposed　iterative　algorithm,　we　presented　new　strategies　for　searching　three　types　of　the　approximate　MPPs　by　merely　using　the　input　and　output　information　of　the　limit　state　function.　In　addition,　the　found　MPPs　can　be　used　for　updating　the　constructed　response　surface　of　the　limit　state　function,　which　in　its　turn　helps　to　find　a　more　accurate　MPP　Findings:　As　illustrated　by　the　examples,　the　proposed　method　provides　excellent　precision　and　convergence　for　the　calculation　results.　Originality:　Three　types　of　the　approximate　MPPs　are　firstly　presented　for　updating　the　constructed　response　surface　of　the　limit　state　function,　whose　input　and　output　information　is　sufficient.　Practical　value:　The　proposed　method　does　not　necessitate　any　requirements　for　the　detailed　format　and　complexity　of　the　limit　state　functions,　which　is　an　advantage.　Hence,　it　is　especially　applicable　to　the　implicit　case　of　complex　engineer　problems.　©　Xiongming　Lai,　Jianhang　Su,　Cheng　Wang,　Yong　Zhang,　He　Huang,　2016.