Space-time fully coupled method is attracting increasing attention in high performance numerical computing area with the fast development of supercomputers. This method is suitable for solving large-scale problems, at the price of solving a huge and ill-conditioned system. To retracing the releasing history of some unsteady pollutant source, we propose a space-time parallel domain decomposition method for efficiently solving the Karush-Kuhn-Tucker(KKT) system , which is induced by reformulating the unsteady inverse source identification problem into an output least square optimization problem with Tikhonov regularizations. This method properly alleviate the ill-condition of the KKT system, compared to sequential quadratic programming(SQP) method, it avoids the ˇ°block Gauss-Seidel processˇ± which iteratively solves three subsystems including the state equation, the adjoint equation and the source equation. Moreover as the highlight of this algorithm, it parallelizes the time marching process into fully coupled scheme in both space and time, thus achieve a high degree of parallelization. Numerical experiments validate that this method is quite effective for recovering unsteady two and three dimensional moving source(s). We also test the parallel efficiency of the algorithm, and obtain a strong scalability result with more than one thousand processors. The method can be readily applied to solve other unsteady inverse problems, and is promising for identifying and tracking pollutant sources in realistic environments.