Abstract: It’s necessary to consider the effects of moving material on neutron transport in some physical processes of extreme engineering problems, where the background material usually has comparable speed with the neutron. Strictly considering the effects introduced by the fluid is extremely complicated. Based on some simplifications, a conservative neutron-hydrodynamic coupling transport was derived, which could capture the main characteristics of neutron transport within moving background materials. The angular phase was discretized using the S_N method. The discretization method of the double angular redistribution of the coupling transport equation was firstly implemented in the 3D cylindrical geometry. Based on this proposed method, the effects of the moving background material on the neutron transport were studied in the steady-state and transient calculations. Numerical results demonstrate that the effects introduced by background material motion cannot be neglected as the material speed starts to approach 1/10 of the neutron speed. Moreover, transient analysis indicates that the background material motion has a considerable impact on the criticality of a system.