Transcritical$CO_2$ systems are under consideration for use as residential/mobile air conditioners. In these systems, an internal heat exchanger is usually adopted to improve both capacity and/or COP of the $CO_2$ system in lower operating pressure range of gas cooler. A program has been developed to analyse the performance of internal heat exchangers using the section-by-section method. The internal heat exchanger of coaxial configuration is first analyzed and fairly good agreements with the data are obtained, And then the internal heat exchanger of multiple circular coil configuration has been investigated. The results obtained from the parametric study provide the guidelines for the initial design and manufacturing concepts of the internal heat exchanger in transcritical $CO_2$ system. Further studies are necessary to develop the heat transfer correlations of carbon dioxide in the tubes to obtain more accurate results.