A graceful labeling of digraph is a one to one function------ --------------------------- s­­­­­­­uch­­­ that each arc in D is labeled with , the re­­sulting arc labels are distinct. A digraph D is called graceful if it admits any graceful labeling. In this p­­­a­per we give a method for constructing a graceful labeling of path digraph and complete bipartite d­­­­igraph .