This letter proposes a robust target localization technique for acoustic underwater wireless sensor networks (UWSNs) that simultaneously experience the stratification effect and the non-line-of-sight (NLOS) bias. Specifically, we develop the range difference (RD)-based majorization minimization expression and its theoretical analysis, which leads to a surrogate function coupling with an iterative form. To figure out the initial estimate of the iteration, the proposed method converts the original localization problem into an RD-based generalized trust-region subproblem (RD-GTRS) after selecting a reference node. Eventually, an RD-based target localization approach (RD-TLA) is presented to iteratively estimate the final location. Simulation results show that the proposed RD-TLA method achieves better localization accuracy compared with other state-of-the-art methods in different scenarios.