In this article, a secret image sharing (SIS) scheme for general access structures (GAS) is designed for distributed multi-user scenario. In the proposed distributed multi-user SIS (DM-SIS), multiple secret images are encoded into shadows which are then distributed to the corresponding storage nodes of a network. By collecting the shadows from nodes, each user is capable of decrypting the corresponding secret image. Fundamentally, we utilize an invertible target matrix, which is initially obtained from the GAS and a base matrix with Vandermonte coordinates, to construct shadows. To deal with the case of non-invertible target matrix, three matrix-adjusting procedures are further introduced. Theoretical analysis, numerical examples, and experiments are provided to verify the feasibility of the proposed technique. When compared to previous methods, the proposed approach can implement GAS sharing strategy in distributed multi-user environment. Meantime, significant improvements on storage overhead and sharing capacity are also achieved.