A numerical simulation of flow of oil blob through a capillary tube constriction is presented. The simulation was run in a 2D axisymmetric model. Water is injected at the inlet to mobilize oil blob placed near the capillary tube constriction. Transient flow images were used to understand the flow evolution process. Results from the study show that pulsed injection effectively assisted to squeeze out the oil blob through the capillary tube constriction with shorter time compared to continuous injection. Pulsed injection reduced the time required for the first droplet to cross the capillary tube constriction by about 3 folds compared to continuous injection. In addition, the droplet that crossed the constriction is larger when the flow was pulsed. In both cases, there is a reverse flow in the opposite direction of the injection. However, the severity of the reverse flow is stronger in the case of continuous injection. Immediately downstream the constriction, there is an adverse pressure gradient zone during continuous injection which limits the mobility of droplet that crossed the constriction. However, in the case of pulsed injection, there is a favorable pressure gradient zone immediately downstream the constriction. This zone expedites mobility of droplets that cross the constriction by transporting them further downstream through suction effect. Apparently, pulsed injection eases off the adverse pressure gradient and allowed more volume of oil to pass through the constriction. Within about two periods of pulsation, 84% of original oil placed at the beginning crossed the constriction compared to only 35% in the case of continuous injection. Even though the same amount of water was injected in both cases, pulsed injection clearly altered the flow behavior. The observation from this study may be extended to more complex flows in order to tailor the method for certain specific applications, such as flow of residual oil through a reservoir.