RFID-based localization has received considerable attention within the healthcare industry and has made a major impact on the healthcare system in hospitals. In this paper, we propose a new location tracking algorithm that aims to improve the accuracy of indoor localization for healthcare applications. In our approach, a cost function associated with a shape constraint factor is used to find the optimal reference tag positions that enclose the tracking tag. The cost function consists of the similarity and disparity of signal strength between the tracking and reference tags, as well as geometrical correlation properties. The experimental results indicate that the proposed shape constraint algorithm provides considerable improvement in average estimation error as compared with existing methods. We believe that this new algorithm is of potential value in dynamic location tracking of objects for healthcare applications.