Let u and v be two fixed vertices. Connect u and v by b internally disjoint paths of length a , the resulting graphs denoted by P_a,b.Kathiresan showed that P_2r,2m-1 is graceful and conjectured that P_a,b is graceful except for (a,b)=(2r+1,4s+2).Yang showed that P_2r+1,2m-1 are graceful. In this paper ,P_3，4m is proved to be graceful. So we prove the conjecture for a=3.