In this paper we study the trajectories of test particles in a geometry that is the nonlinear electromagnetic generalization of the Reissner–Nordström black hole. The solution was originally derived by García, Salazar and Plebañski (1984 Nuovo Cimento 84 65–90). The studied spacetime is an Einstein–Born–Infeld solution, nonsingular outside a regular event horizon and characterized by three parameters: mass M, charge Q and the Born–Infeld parameter b related to the magnitude of the electric field at the origin. Asymptotically it is a Reissner–Nordström solution.