This paper focuses on the admissible consensus problem for heterogeneous descriptor multi-agent systems. Based on algebra, graph and descriptor system theory, the necessary and sufficient conditions are proposed for heterogeneous descriptor multi-agent systems achieving admissible consensus. The provided conditions depend on not only the structure properties of each agent dynamics but also the topologies within the descriptor multi-agent systems. Moreover, an algorithm is given to design the novel consensus protocol. A numerical example demonstrates the effectiveness of the proposed design approach.