Based on the extending symmetry group approach and symbolic computation, some finite symmetry group solutions of the nonlinear Schrdinger (NLS) equations with various variable coefficients are investigated. On the basis of the extending symmetry group, determining equations are discussed in three kinds of cases, then six kinds of symmetry transformations are constructed and the relations between the standard (3+1)-D NLS equation and (3+1)-D variable coefficient NLS equations are derived. By using these symmetry transformations, rich exact solutions of some (3+1)-D variable coefficient NLS equations are obtained from the standard (3+1)-D NLS equation.