Polymer flooding is employed to prevent immiscible viscous fingering between oil and water. If the polymer injection concentration is decreased rapidly, there is a high chance that fast growing miscible viscous fingers will pierce through the polymer bank and enter the oil bank. This is very detrimental to oil production. We performed numerical modeling of polymer flooding in one-quarter of a five-spot system. Due to the nonuniform flow field in a five-spot setup, the fingering patterns are very different and miscible fingers are more detrimental in this case than in a rectangular domain. In this paper we quantify the impact of injection concentration and duration of polymer flooding on the growth rate of miscible and immiscible viscous fingers. Besides decrease and increase of immiscible and miscible viscous finger growth at the front and rear of polymer banks respectively, we have shown that the residual oil saturation decreases for higher injection concentrations. However for high injection concentrations, polymer should be injected for a long duration so that the width of the polymer bank is large and miscible fingers cannot cause short-circuiting. Since injection at constant concentration for a long duration is not optimal, simulations for different multi-step injection were performed. Our results demonstrate that arbitrary decreases in polymer injection concentration are not effective for enhancing oil recovery. The ideal polymer injection scheme suggested by our simulations should involve an initial constant rate, followed by a gradual decrease. This is mainly to overcome the retardation due to adsorption of the polymer. © 2018 Elsevier Ltd