Non-intrusive load monitoring (NILM) is an approach that helps residents obtain detailed information about household electricity consumption and has gradually become a research focus in recent years. Most of the existing algorithms on NILM build energy disaggregation models independently for an individual appliance while neglecting the relation among them. For this situation, this article proposes a multi-chain disaggregation method for NILM (MC-NILM). MC-NILM integrates the models generated by existing algorithms and considers the relation among these models to improve the performance of energy disaggregation. Given the high time complexity of searching for the optimal MC-NILM structure, this article proposes two methods to reduce the time complexity, the k-length chain method and the graph-based chain generation method. Finally, we use the Dataport and UK-DALE datasets to evaluate the feasibility, effectiveness, and generality of the MC-NILM.