Fast data synchronization in wireless ad hoc networks is a challenging and critical problem. It is fundamental for efficient information fusion, control and decision in distributed systems. Previously, distributed data synchronization was mainly studied in the latency-tolerant distributed databases, or assuming the general model of wireless ad hoc networks. In this paper, we propose a pair of linear network coding (NC) and all-to-all broadcast based fast data synchronization algorithms for wireless ad hoc networks whose topology is under operator's control. We consider both data block selection and transmitting node selection for exploiting the benefits of NC. Instead of using the store-and-forward protocol as in the conventional uncoded approach, a compute-and-forward protocol is used in our scheme, which improves the transmission efficiency. The performance of the proposed algorithms is studied under different values of network size, network connection degree, and per-hop packet error rate. Simulation results demonstrate that our algorithms significantly reduce the times slots used for data synchronization compared with the baseline that does not use NC.