Blockchain relies on an unstructured Peer-to-Peer （P2P） overlay network for the propagation of transactions and blocks. In this network structure， propagation is delayed， and the long-tail propagation problem is significant， which lead to inconsistencies in the information stored by nodes， that is the phenomenon of blockchain forks. Forks not only waste computational resources in the entire blockchain network， but also introduce a series of security issues. To reduce propagation delays in blockchain networks， a Neighbor Selection scheme based on Multi-stage Propagation （NSMP） was proposed to optimize the network topology by selecting neighbor nodes. Firstly， the nodes’ Outbound neighbors were divided into strong and weak propagators based on two factors： propagation ability and proximity， and different neighbor selection schemes were applied at different stages of network propagation， thereby reducing propagation hops and shortening propagation time. At the same time， the long-tail propagation problems in both existing and default schemes were further solved. Finally， the propagation ability of nodes was quantified by a fitting function based on node local characteristics， proximity information of the nodes was quantified using the Ping protocol， and the designed scheme was tested through simulation experiments using the network simulator SimBlock. Experimental results show that NSMP reduces the fork rate by 52.17% compared to the default scheme， demonstrating the feasibility and effectiveness of NSMP. Besides， according to the simulation data of experiments， the optimal parameter setting for the distribution of neighbor node proximity was determined.