The robust average consistency theory is ideal for building time synchronization in the dynamic and distributed networks, however it remains the major challenge due to the iteration. Existing consensus-based approaches converge slowly, although they are reliable even in dynamic networks. It is thus unreasonable to implement these algorithms in a large-scale wireless network. Motivated by this consideration, we note that the graph theory-based theory suggests that the greater the algebraic connectivity, the faster the convergence, thereby leading to the proposal of multi-hop average consensus time synchronization (MACTS) with innovative implementation in consideration of the features of wireless sensor network. To accelerate the synchronization convergence without changing the network topology, we present a packet fast forwarding model to generate virtual communication links among multi-hop nodes, meanwhile, an attenuation methods for the forwarding model is designed to balance the accuracy and cost of synchronization. We compensate relative clock offset estimates by transmitting delay estimates to achieve accurate synchronization. Moreover, based on the popular one-way broadcast model, the proposed MACTS is easy to implement. The experimental results indicate that MACTS is more accurate and converges much faster than the typical average consistency synchronization algorithm.