Recently, many time synchronization algorithms are divergent with random bounded communication delay. Based on the Average TimeSynch (ATS), this paper analyzes the synchronization of skew and offset to find out the reason for the divergence of the synchronization. By changing the method of estimating the relative offset, the convergence of the skew synchronization is ensured. In the offset synchronization, by calculating the synchronization error of the node, it is proved that the offset synchronization error under delay is bounded. Finally, simulation cases show that the proposed time synchronization algorithm with random bounded delay may guarantee the synchronization convergence and boundedness of the synchronization error if the network topology is connected.