The heat transfer characteristics of an internal heat exchanger for $CO_2$ refrigeration cycle are numerically investigated. The numerical model is verified using the published experimental results for the concentric tube type internal heat exchanger. The Hardy-Cross Method gives very good agreement between the calculation and experimental results on the heat transfer rates and exit temperatures. Also, appropriate combination of heat transfer correlations is found. The operating parameters of the heat exchanger are calculated at transcritical region of $CO_2.$ The heat transfer rate of the counter flow type heat exchanger shows the $32\%$ greater than that of the parallel flow type heat exchanger. The increase of heat exchanger length enhances the heat transfer rate. The thermodynamic characteristics and heat transfer coefficient of $CO_2$ in the internal heat exchanger are estimated.