A parametric study on the scroll wrap configuration factors of a $CO_2$scroll compressor for heat pump water heater has been carried out. Since there are 7 scroll wrap design parameters and 5 equations relating them, two of the design parameters can be selected as independent parameters. In this study, the wrap thickness and orbiting radius are chosen as independent ones. Computer simulation program has been used to estimate the compressor performance at various combinations of the scroll wrap design parameters. It has been found that there exists optimum combination of the wrap parameters for the highest compressor performance over analyzed ranges of the design parameters.