Three dimensional transient thermal analysis of an air-cooled module that contains prismatic Li-ion cells next to a special kind of aluminum pin fin heat sink whose heights of pin fins increase linearly through the width of the channel in air flow direction was studied for thermal management of Lithium-ion battery pack. The effects of pin fins arrangements, discharge rates, inlet air flow velocities, and inlet air temperatures on the battery were investigated. The results showed that despite of heat sinks with uniform pin fin heights that increase the standard deviation of the temperature field, using this kind of pin fin heat sink compare to the heat sink without pin fins not only decreases the bulk temperature inside the battery, but also decreases the standard deviation of the temperature field inside the battery as well. Increasing the inlet air temperature leads to decreasing the standard deviation of the temperature field while increases the maximum temperature of the battery. Furthermore, increasing the inlet air velocity first increases the standard deviation of the temperature field till reaches to the maximum point, and after that decreases. Also, increasing the inlet air velocity leads to decrease in the maximum temperature of the battery.