In this correspondence, we develop an algorithm for maximum likelihood (ML) source localization using received signal strength (RSS) measurements. Unlike the conventional methods that resort to first-order Taylor series approximations to linearize the RSS data model, we use the actual nonlinear data model and propose an algorithm for solving the associated ML estimation problem. More specifically, we reformulate the original ML minimization as a min–max problem, which we solve using a majorization–minimization technique. Each iteration of the resultant algorithm involves solving a simple convex problem and monotonically decreases the (negative) ML criterion. Several numerical simulation results illustrate the accuracy of the proposed method when compared against state-of-the-art methods.