The received signal strength (RSS) based target localization problem in underwater acoustic wireless sensor networks (UWSNs) is considered. Two cases with respect to target transmit power are considered. For the first case, under the assumption that the reference of the target transmit power is known, we derive a novel weighted least squares (WLS) estimator by using an approximation to the RSS expressions, and then transform the originally non-convex problem into a mixed semi-definite programming/second-order cone programming (SD/SOCP) problem for reaching an efficient solution. For the second case, there is no knowledge on the target transmit power, and we treat the reference power as an additional unknown parameter. In this case, we formulate a WLS estimator by using a further approximation, and present an iterative ML and mixed SD/SOCP algorithm for solving the derived WLS problem. For both cases, we also derive the closed form expressions of the Cramer–Rao Lower Bounds (CRLBs) on root mean square error (RMSE). Computer simulation results show the superior performance of the proposed methods over the existing ones in the underwater acoustic environment.