IEEE 1588 is used for clock synchronization in a networked measurement and control system of the distribution grid. It plays an important role in the packet-based network synchronization mechanism. However, the performance of the conventional IEEE 1588 synchronization algorithm is affected by the asymmetric link and random delay problems. This paper proposes an improved IEEE 1588 based synchronization scheme involves two different random delay models: the Gaussian random delay model and the exponential random delay model. And the time offset and the maximum likelihood estimators of the two random delay models are derived. The results show that the clock offset estimation performance depends on the ratio of the random delay of the model and the size of the data packet transmitted. As is shown in the simulation results, the solution to the asymmetric links and random delay issue compared with the traditional IEEE 1588 clock synchronization method and burst transmission scheme obtains better performance.