In this paper, we reduced the governing equation describing the one-dimensional granular crystals of elastic spheres to a continuous equation by small deformation and long wave approximation. Then, the G’/G-expansion method is applied to this continuous equation, and the exact solitary wave solutions with arbitrary parameters are obtained. Compared with other papers, the solutions obtained in this paper are more extensive and contains more parameters. The simultaneous existence of exact solitary wave solutions can help us study the propagation of shock waves in one-dimensional granular crystals of elastic spheres. At the same time, it has important theoretical significance in nondestructive testing with non-linear wave.