The stability of the waterfront in a heterogeneous porous medium and in the absence of gravity effects is controlled by capillary and viscous forces. Under oil-wet conditions, waterflood is a drainage process and the displacement front advances in zones with larger pores where capillary forces are lower, and the rate of displacement is higher compared to zones with smaller pores. Hence, in a waterflood process, a transition zone is formed where the water saturation gradually decreases from a trailing front to the leading end of advanced water fingers. In a heterogeneous medium, oil-water capillary pressure fluctuates due to variations of pore sizes in flooding paths. The difference in the capillary pressures between leading and trailing zones can help with the stability of the waterfront when the capillary pressure in frontal zones is increased by displacing oil through smaller pores. However, this mechanism creates a limited pressure gradient in the oil phase, so the waterfront instabilities continue to grow, especially at the adverse mobility ratio and high displacement rates. In this study, different oil samples with low, medium and high viscosities are displaced by water in an oil-wet medium containing pore-level heterogeneities. Herein, the effect of flow swing, which is introduced to the direction of oil-water displacement, on waterflood performance is investigated. Under flow-swing conditions, we reverse the fluid flow direction periodically; however, the overall volume of injected water is maintained the same for all scenarios by adjusting the periods of the forward and reverse steps. The flow reversal promotes the refill of water paths with oil, hence attenuating the advanced fingers. Consequently, the sweep efficiency of waterflood is improved and higher oil sweep efficiency is obtained at the time of breakthrough. The flow-swing mechanism is more effective when oscillations of capillary pressure result in a faster flow of oil between trailing and leading zones, thus decreasing the waterfront instabilities. The new process can be optimized and utilized at larger scales for improving the sweep efficiency of flooding operations.