Abstract: The fission fragment rocket engine (FFRE) that is a new novel concept of space propulsion was present by Grassmere Dynamics LLC, USA in 2005. The NIAC program of NASA was instrumental in nurturing this concept. The fissile dust plasma of nanoscale was designed in fission reactor. The charged fission fragments with high energy escape from the magnetic field resulting in thrust and specific impulse of million seconds. The physics process in the FFRE was studied, the critical mass and fission fragments transport were calculated and simulated by the transport Monte Carlo program MCNP and SRIM, and the temperature of dust was calculated with thermal spike model. The optimal design is the reactor with californium dust plasma and beryllium reflector in constraint magnetic field, and the escape rate will be more than 60%.