Abstract: The reconstruction problem of spatio-temporal signals can be cast as recovering differential smooth time-varying graph signals. For the optimization problem, the existing distributed algorithm based on gradient descent method shows slow convergence when the condition number of the Hessian matrix of the problem is large which leads to a large reconstruction error when the maximum iteration number is limited in an observation interval. Therefore, an online distributed reconstruction algorithm based on approximate Newton′s method is proposed in the paper, whose principle is to decompose the original optimization problem into a series of local problems on subgraphs through subgraph decomposition and find these solutions, and then obtain the approximate global optimal solution via fusion average of local solutions between each subgraph. According to the gap between the approximate solution and the actual one, it can be proved that the decompostion and fusion matrix obtained in this way is sparse and can be regarded as the approximate Hessian inverse. Hence, the algorithm replaces the approximate matrix into the classical Newton iterative formula which can be implemented in a distributed manner due to the structural sparsity of the approximate matrix. Simulation results show that the proposed algorithm has faster convergence rate and smaller reconstruction error, and requires less communication cost compared with the existing algorithm.