<p>Under investigation is a generalized massive Thirring model, which can be directly degenerated into the standard massive Thirring model describing the propagations of Dirac solitons in the quantum field theory and solitons in optical Bragg gratings. On basis of the <i>N</i>-fold classical Darboux transformation (DT), we establish the (<i>n</i>,<i>N</i>-<i>n</i>)-fold generalized perturbation DT by means of the limiting technique, and put forward the general <i>N</i>th-order localized wave solution in a compact determinant form. Explicitly, the soliton solutions under zero background and rogue wave solutions under nonzero background from first to third order are presented by means of the (1,<i>N</i>-1)-fold generalized perturbation DT. Moreover, the second-order hybrid soliton-soliton solutions and hybrid rogue wave-breather solutions are obtained by virtue of the (2,<i>N</i>-2)-fold generalized perturbation DT. In particular, the bell-shaped solitons, oscillating solitons, bound-state solitons and rogue waves with triangular and pentagonal patterns are shown graphically.</p>