We apply the method of Hasenfratz and Niedermayer to analytically construct perfect lattice actions for the Gross-Neveu model. In the large N limit these actions display an exactly perfect scaling, i.e. cut-off artifacts are completely eliminated even at arbitrarily short correlation length. Also the energy spectrum coincides with the spectrum in the continuum and continuous translation and rotation symmetries are restored in physical observables. This is the first (analytic) construction of an exactly perfect lattice action at finite correlation length. ((orig.)).