The　notion　of　penalty　has　been　introduced　into　many　combinatorial　optimization　models.　In　this　paper,　we　consider　the　submodular　vertex　cover　problems　with　linear　and　submodular　penalties,　which　are　two　variants　of　the　submodular　vertex　cover　problem　where　not　all　the　edges　are　required　to　be　covered　by　a　vertex　cover,　and　the　uncovered　edges　are　penalized.　The　problem　is　to　determine　a　vertex　subset　to　cover　some　edges　and　penalize　the　uncovered　edges　such　that　the　total　cost　including　covering　and　penalty　is　minimized.　To　overcome　the　difficulty　of　implementing　the　primal-dual　framework　directly,　we　relax　the　two　dual　programs　to　slightly　weaker　versions.　We　then　present　two　primal　dual　approximation　algorithms　with　approximation　ratios　of　2　and　4,　respectively.　(C)　2016　Elsevier　B.V.　All　rights　reserved.