A finite-difference scheme for a class of convection-diffusion problems in 2D space is presented and analyzed. The problem under consideration is a singularly-perturbed time-dependent partial differential equations problem with convection term positive in both space directions, and a nonnegative reaction term. The proposed method is uniformly convergent with respect to diffusion parameter, and reaches almost second-order precision in space. The authors argue that the developed method is applicable to a wider class of problems than the method is originally designed for.