We investigate a localization problem using time-difference-of-arrival measurements with unknown and bounded measurement errors. Different from most existing algorithms, we consider the minimization of the worst-case position estimation error to improve the robustness of the algorithm. The localization problem is formulated as a nonconvex optimization problem. We adopt semidefinite relaxation to relax the original problem into a convex optimization problem, which can be solved using existing semidefinite program solvers. Simulation results show that our proposed algorithm has lower worst-case position estimation error than other existing algorithms.