A systematic expansion scheme that goes beyond the Gutzwiller-type approximation is developed for generalized Gutzwiller wave functions. The expansion satisfies sum rules and symmetries of the trial wave function in a self-consistent way. We apply the scheme to an antiferromagnetic generalization of the Gutzwiller wave function for the one-dimensional Hubbard model. We find good agreement with known results from variational Monte Carlo calculations. We also demonstrate that the expansion scheme converges rapidly.