As a centralized location for computer systems, data centers provide high-performance computing hardware, storage devices, and network facilities for collaborative computing. The node-disjoint paths can be used to implement multi-path transmission in data center networks, which provide multiple high-quality transmission paths and improve the performance of the network. Moreover, the disjoint paths can also provide redundant transmission paths, which enhance the fault tolerance of the network. The EHDC network is a novel server-centric and highly scalable data center network based on exchanged hypercube, and its logical structure is ED(s, t). In this paper, we propose the algorithm NDPath to construct the node-disjoint paths between two distinct nodes when the two nodes are in the same ED s in ED(s, t). Moreover, we analyze the maximum length of the disjoint paths. Experimental results show that our proposed algorithm performs better than the classical algorithm Dijkstra in the Average Running Time (ART) and is very close to that in the Average Path Length (APL).