Background: The scattering of H- and E-polarized plane waves by a two-dimensional (2-D) parabolic reflector made of graphene and placed in the free space is studied numerically. Methods: To obtain accurate results we use the Method of Analytical Regularization. Results: The total scattering cross-section and the absorption cross-section are computed, together with the field magnitude in the geometrical focus of reflector. The surface plasmon resonances are observed in the H-case. The focusing ability of the reflector is studied in dependence of graphene’s chemical potential, frequency, and reflector’s depth. Conclusions: It is found that there exists an optimal range of frequencies where the focusing ability reaches maximum values. The reason is the quick degradation of graphene’s surface conductivity with frequency. © 2017, The Author(s).