Space nuclear reactor power (SNRP) using a gas-cooled reactor (GCR) and a closed Brayton cycle (CBC) is the ideal choice for future high-power space missions. To investigate the safety characteristics and develop the control strategies for gas-cooled SNRP, transient models for GCR, energy conversion unit, pipes, heat exchangers, pump and heat pipe radiator are established and a system analysis code is developed in this paper. Then, analyses of several operation conditions are performed using this code. In full-power steady-state operation, the core hot spot of 1293 K occurs near the upper part of the core. If 0.4 $ reactivity is introduced into the core, the maximum temperature that the fuel can reach is 2059 K, which is 914 K lower than the fuel melting point. The system finally has the ability to achieve a new steady-state with a higher reactor power. When the GCR is shut down in an emergency, the residual heat of the reactor can be removed through the conduction of the core and radiation heat transfer. The results indicate that the designed GCR is inherently safe owing to its negative reactivity feedback and passive decay heat removal. This paper may provide valuable references for safety design and analysis of the gas-cooled SNRP coupled with CBC.