The purpose of this paper is to investigate the effect of injection rate, gravity force and connate water saturation on the mechanism of gravity drainage.Gravity drainage is the most important mechanism in oil recovery from the fractured reservoirs. During gas injection gravity drainage may either become more effective or retard the process. Finding the optimum injection rate is our main goal in this study.In our experiments nitrogen and kerosene were used as gas and oil respectively. The core samples were prepared from outcrop of Asmari formation of Iran, which was a fractured carbonate rock.The injection gas rate is an important factor affecting on the oil recovery .We found a critical rate in which the gas rate is lower or higher than critical, the oil recovery decreases. However the recovery factor at critical rate is the maximum .This phenomena was discussed based on the competition of different forces of viscous, capillary and gravity .These forces cause the displacement change from the stable piston like displacement to an unstable trapping displacement. Observation showed that different amount of the gravity forces have no effect on oil recovery before gas breakthrough; however, with more gravity force, more oil production was observed after breakthrough. Also, we observed irreducible water saturation change during gas injection in our carbonate rocks.