In a modern high speed drawing process of optical fibers, it is necessary to use helium as a cooling gas in a glass fiber cooling unit in order to sufficiently cool down the fast moving glass fiber freshly drawn from the heated silica preform in the furnace. Since the air is entrained unavoidably when the glass fiber passes through the cooling unit, the helium is needed to be injected constantly into the cooling unit. The present numerical study investigates and analyzes the air entrainment using an axisymmetric geometry of glass fiber cooling unit. The effects of helium injection rate and direction on the air entrainment rate are discussed in terms of helium purity of cooling gas inside the cooling unit. For a given rate of helium injection, it is found that there exists a certain drawing speed that results in sudden increase in the air entrainment rate, which leads to the decreasing helium purity and therefore the cooling performance of the glass fiber cooling unit. Also, the helium injection in aiding direction is found to be more advantageous than the injection in opposing direction.