The MCNPX Monte-Carlo code has been used to model the neutron transport in a sub-critical fast fission reactor driven by a fusion neutron source. A stellarator-mirror device is considered as the fusion neutron source. The principal composition for a fission blanket of a mirror fusion–fission hybrid is devised from the calculations. Heat load on the first wall, the distribution of the neutron fields in the reactor, the neutron spectrum and the distribution of energy release in the blanket are calculated. The possibility of tritium breeding inside the installation in quantities that meet the needs of the fusion neutron source is analyzed. The portion of the plasma column generates fusion neutrons that mainly do not reach the fission reactor core is proposed to be surrounded by a vessel filled with borated water to absorb the flying out neutrons. The flux of the neutrons escaping from the device to surrounding space is also calculated.