We present a distributed and decentralized algorithm for graph signal inpainting. The previous work obtained a closed-form solution with matrix inversion. In this paper, we ease the computation by using a distributed algorithm, which solves graph signal inpainting by restricting each node to communicate only with its local nodes. We show that the solution of the distributed algorithm converges to the closed-form solution with the corresponding convergence speed. Experiments on online blog classification and temperature prediction suggest that the convergence speed of the proposed distributed algorithm is competitive with that of the centralized algorithm, especially when a graph tends to be regular. Since a distributed algorithm does not require to collect data to a center, it is more practical and efficient.