In　this　paper,　we　study　a　class　of　online　continuous　optimization　problems.　At　each　round,　the　utility　function　is　the　sum　of　a　weakly　diminishing-returns　(DR)　submodular　function　and　a　concave　function,　certain　cost　associated　with　the　action　will　occur,　and　the　problem　has　total　limited　budget.　Combining　the　two　methods,　the　penalty　function　and　Frank-Wolfe　strategies,　we　present　an　online　method　to　solve　the　considered　problem.　Choosing　appropriate　stepsize　and　penalty　parameters,　the　performance　of　the　online　algorithm　is　guaranteed,　that　is,　it　achieves　sub-linear　regret　bound　and　certain　mild　constraint　violation　bound　in　expectation.