We　study　a　precedence-constrained　identical　parallel　machine　scheduling　problem　with　rejection.　There　is　a　communication　delay　between　any　two　jobs　connected　in　the　precedence　network　where　jobs　may　be　rejected　with　penalty.　The　goal　is　to　minimize　the　sum　of　the　makespan　and　the　rejection　cost.　We　propose　two　3-approximation　algorithms　for　this　problem　under　linear　and　submodular　rejection　costs　respectively.　These　two　algorithms　are　both　based　on　linear　programming　rounding　technique.