We consider two-dimensional (2-D) thin dielectric parabolic reflector, covered with graphene from both sides, illuminated symmetrically by an E-polarized electromagnetic plane wave. Our aim is to estimate the focussing ability of such a composite reflector depending on the graphene parameters. We use a version of the two-side generalized boundary condition, modified for a thin multilayer case. The scattering is formulated as an electromagnetic boundary-value problem; it is cast to a set of two coupled singular integral equations that are further subjected to analytical regularisation based on the known Riemann–Hilbert problem solution. Thanks to this procedure, the numerical results are computed from a Fredholm second-kind matrix equation that guarantees convergence and provides easily controlled accuracy. In the lower part of the THz range, high values of the focusing ability are observed even for a thin reflector; they are greater than for a purely dielectric reflector and a free standing graphene reflector. On the other hand, a regime of almost full transparency, intrinsic for the dielectric layer, can spoil focusing ability. Novel aspect is that the location in frequency of this effect can be controlled, in wide range, by changing the chemical potential of graphene.