A pendulum damping device for a motor vehicle transmission, having at least one pendulum mass (33), a central part (33a) of which is mounted movably on a support (26) capable of pivoting around an axis, and having at least one roller (36) mounted radially between the radially outer periphery of the central part (33a) and a radially outer part of the support (26), in such a way that during operation, the central part (33a) of the pendulum mass (33) abuts radially outwardly against the roller (36), the latter (36) in turn abutting radially outwardly against the support (26). The pendulum mass (33) comprises at least one lateral part (33b) fastened to the central part (33a) and designed so that the center of gravity of the pendulum mass (33) is situated radially outside the contact regions between the central part (33a) of the pendulum mass (33) and the roller (36).