Abstract: The drop critical safety at the launch phase is the key point and difficult point in the design of space fast reactor. One of the general methods to ensure drop critical safety is using spectral shift absorption material as the structure material. The Mo-Re alloy is usually used as spectral shift absorption material and the structure material with its excellent spectral shift performance and high temperature performance. The study was focused on Prometheus basic core scheme, using MCNP code, calculated and analyzed the effect of Mo-Re alloy on drop critical safety and its mechanism in the different drop conditions. The results suggest that the drop condition has different effects on the critical safety with the different contents of Re. The strengthened resonance absorption caused by softenspectrum and the increase of Re content are the main factors of the change of the worst drop condition.