This paper introduces algorithms for the decentralized low-rank matrix completion problem. Assume a low-rank matrix W = [W <sub>1</sub> ,W <sub>2</sub> , ...,W <sub>L</sub> ]. In a network, each agent observes some entries of W <sub></sub> . In order to recover the unobserved entries of W via decentralized computation, we factorize the unknown matrix W as the product of a public matrix X, common to all agents, and a private matrix Y = [Y <sub>1</sub> ,Y <sub>2</sub> , ...,Y <sub>L</sub> ], where Y <sub></sub> is held by agent . Each agent alternatively updates Y <sub></sub> and its local estimate of X while communicating with its neighbors toward a consensus on the estimate. Once this consensus is (nearly) reached throughout the network, each agent recovers W <sub></sub> = XY <sub></sub> , and thus W is recovered. The communication cost is scalable to the number of agents, and W <sub></sub> and Y <sub></sub> are kept private to agent to a certain extent. The algorithm is accelerated by extrapolation and compares favorably to the centralized