In this paper, we study the global clock synchronization problem for wireless sensor networks under unknown exponential delays in the two-way message exchange mechanism. The joint maximum likelihood estimator of clock offsets, clock skews and fixed delays for the network is formulated as a linear programming (LP) problem. Then, based on the alternating direction method of multipliers (ADMM), we propose a fully distributed synchronization algorithm which has low communication overhead and computation cost. Simulation results show that the proposed algorithm achieves better accuracy than consensus algorithm and the distributed least squares algorithm, and can always converge to the centralized optimal solution.