In this work, the differential received signal strength based localization problem is addressed. Based on the measurement model, we present the constrained weighted least squares (CWLS) approach, which is difficult to be solved directly due to its nonconvex nature. However, by performing the semidefinite relaxation (SDR) technique, the CWLS problem can be relaxed into a semidefinite programming problem (SDP), which can be efficiently solved using modern convex optimization algorithms. Moreover, the SDR is proved to be tight, and hence ensures the corresponding SDP find the optimal solution of the original CWLS problem. Numerical simulations are included to corroborate the theoretical results and promising performance.