The propagation of elastic waves in one-dimensional phononic crystals(PCs) which are composed of both functionally graded materials(FGM) and isotropic material has been studied by using the plane wave expansion method. The material properties of FGM are varied according to a well-known rule, such as the exponential function. The influences of the exponential factor of FGM , filling fraction of two kinds of materials and length of materials on the first four normalize frequency gaps location and width are discussed, respectively. These results provide the theoretical basis and guidance for PCs with FGM widely using in engineering practice.