Abstract: 3D-cylinder reactor core neutron space-time kinetics is simulated with an improved quasi-static method. The program is developed. In a supposable 250 MW modular HTGR model, the core neutron space-time kinetics is simulated. Calculated results obtained from this program and CITATION code agree well with each other at initiatory state. Variance of the core reactivity, average neutron flux of each group, and relative power with time is computed.