As　a　convenient　and　economic　computing　model,　cloud　computing　promotes　the　development　of　intelligence.　Solving　the　workflow　scheduling　is　a　significant　topic　to　promote　the　development　of　the　cloud　computing.　In　this　work,　an　Actor-Critic　architecture　is　utilized　to　solve　this　problem　achieving　the　task　executive　time　minimization　under　the　task　precedence　constraint.　It　is　similar　to　the　list-based　heuristic　algorithm　which　includes　the　task　prioritizing　phase　and　task　allocation　phase.　However,　the　results　of　the　two　phases　interact　with　each　other.　In　the　task　prioritizing　phase,　given　a　workflow　represented　as　the　data　communication　time　matrix　and　task　computation　time　matrix,　a　distribution　over　different　task　permutations　by　the　improved　Pointer　network　can　be　predicted.　Then,　the　heuristic　algorithm　based　on　the　HEFT　achieves　the　task　allocation　to　get　the　task　executive　time.　Using　negative　task　executive　time　as　the　reward　signals,　the　model　parameters　by　a　policy　gradient　method　in　the　first　phase　can　be　optimized.　The　simulation　experiment　is　done　from　the　task　executive　time,　and　the　results　shows　that　the　workflow　scheduling　by　the　deep　reinforcement　learning　is　more　effective　comparing　with　other　four　single　objective　heuristic　algorithms.