An exact similarity solution of the steady mixed convection flow of a viscous and incompressible fluid in the vicinity of two-dimensional stagnation-point with a second-order slip condition has been investigated. Using appropriate similarity variable, the Navier–Stokes equations coupled with the energy equation governing the flow and heat transfer are reduced to a system of nonlinear ordinary (similarity) equations, which are well-posed. These equations are solved numerically in the buoyancy assisting and opposing flow regions. It is found that a reverse flow region develops in the buoyancy opposing flow case, and dual (upper and lower branch) solutions are found to exist in the case of opposing flow region for a certain range of the negative values of the mixed convection parameter. A stability analysis has been performed, which shows that the upper branch solutions are stable and physically realizable in practice, while the lower branch solutions are not stable and, therefore, not physically realizable in practice. The numerical results have been compared with those reported in the literature, the agreement being excellent.