In this paper, the application of H∞ optimal control theory to GPS (Global Positioning System) receiver tracking loops is investigated. We design an H∞ controller for the receiver tracking loop. The H∞ controller is particularly attractive because it is a robust design in the sense that small disturbances lead to small tracking errors. Furthermore, it easily accommodates the inclusion of plant uncertainties as part of the plant model. By adding unstructured or structured perturbations to the plant model, it is possible to design controller that ensure stability robustness and performance robustness of the closed-loop system. In order to apply the H∞ optimal design, we first rewrite the GPS receiver tracking loop into a two-input two-output generalized plant model. By using a software-based GPS L5 signal generator, various levels of disturbances are derived as test inputs to evaluate the performance of the resulting tracking loop.