In　order　to　solve　the　workflow　time-cost　optimization　problem　under　deadline　restrictions　represented　by　directed　acyclic　graph　(DAG)　in　computation　grids,　a　novel　heuristics　algorithm　called　relative　time-cost　rate(RTCR)was　proposed.　Firstly　the　preliminary　program　was　obtained　by　scheduling　coefficient,　then　the　scheduling　was　optimized　gradually:　when　the　deadline　exceeded,　the　node　with　the　slowest　cost-decreased　service　was　rescheduled,　the　selected　service　had　the　maximum　positive　RTCR　value,　otherwise　the　node　with　the　fastest　cost-increased　service　was　rescheduled,　the　selected　service　had　the　maximum　negative　RTCR　value.　The　proposed　method　simultaneously　guaranteed　deadline　restrictions　and　reduced　total　cost.,　the　RTCR＇s　effectivenss　was　revealed　by　comparing　with　minimum　critical　path　(MCP),　deadline　top　level　(DTL)　and　deadline　bottom　leve　(DBL　l).