Many　workflow　applications　often　have　the　timing　constraints　such　that　each　processing　of　a　workflow　needs　to　be　finished　within　its　deadline.　There　have　been　some　work　to　improve　the　performance　of　time-constrained　workflow　processing.　Previous　work　mainly　considered　to　meet　the　execution　time　request　of　the　critical　path　tasks　or　all　of　the　tasks　both　on　the　critical　path　and　on　the　non-critical　path.　Few　of　them,　however,　have　taken　into　account　the　fact　that　successful　execution　of　workflow　within　its　deadline　is　also　affected　by　＇normal　state＇　and　＇abnormal　state＇　of　grid　resources　occurring　in　successive　turns　and　by　the　relative　difference　in　execution　time　between　tasks　on　the　critical　path　and　tasks　on　the　non-critical　path.　To　solve　the　problems,　some　new　definitions,　such　as　critical　region　and　reliability　of　critical　region　are　defined,　and　then　a　new　resource　allocating　algorithm　is　proposed　in　terms　of　the　finite-state　continuous-time　Markov　process　through　selecting　a　resource　combination　scheme　which　has　the　lowest　expenditure　under　certain　credit　level　of　the　resource　reliability　in　the　DAG-based　workflow.　Compared　with　previous　algorithms,　this　method　is　much　more　efficient　in　resource　allocating,　and　almost　no　degrading　in　successful　grid　workflow　execution　rate.　The　simulation　shows　the　validity　of　the　new　algorithm.