The 1N expansion method for the degenerate Anderson model is formulated. N is the degeneracy factor of one of the f-electron configurations. Various ground-state properties are calculated. Excellent agreement with the result of Bethe ansatz for N=6 is shown. The rate of convergence of the series is analyzed. The merit and inadequacy of the method are discussed. At zero temperature the ratio of the magnetic susceptibility and the specific-heat linear coefficient is shown to lie within a range of 1 and 1+(N-1)-1.