Using the modified CK's direct method, general symmetry group, Lie symmetries and corresponding vector fields of a (3+1)-dimensional nonlinear evolution equation are obtained. The relationship between new solutions and old ones of the (3+1)-dimensional nonlinear evolution equation is built by applying the results. 80me new exact solutions of the (3+1 )-dimensional nonlinear evolution equation are obtained. As for the close relationship between symmetries and conservation laws, the infinite conservation laws of the (3+1)-dimensional nonlinear evolution equation are found.