Source localization is a fundamental task in many areas such as wireless sensor networks, telecommunications and mobile communications. This is commonly achieved with the use of distance measurements between the source and receivers, and they are usually converted from the time-of-arrival or received signal strength information. Although numerous methods have been proposed for distance-based source localization, most of them assume that the receiver positions are known exactly, which may not be valid in practice. In this paper, a complex-valued semidefinite relaxation (SDR) algorithm is devised for source localization in the presence of receiver position uncertainties. Reduction of the algorithm complexity is also considered. The estimation accuracy and computational attractiveness of the proposed SDR scheme are demonstrated via computer simulations.