The most state-of-art time-difference-of-arrival (TDOA) localization algorithms are performed under the assumption that all the nodes are synchronized. However, for a widely distributed wireless sensor networks (WSNs), time synchronization between all the nodes is not a trival problem. In this paper, we study the problem of source localization using signal TDOA measurements in the system of nodes part synchronization. Starting from the maximum likelihood estimator (MLE), we develop a semidefinite programming (SDP) approach. Besides, we extend the SDP algorithm to the case of non-accurate sensor position. Simulation results validate the localization performance of the proposed SDP algorithms.