This study investigates the neutronics design aspects of a hybrid fusion-fission energy system called the Laser Fusion-Fission Hybrid (LFFH). A LFFH combines current Laser Inertial Confinement fusion technology with that of advanced fission reactor technology to produce a system that eliminates many of the negative aspects of pure fusion or pure fission systems. When examining the LFFH energy mission, a significant portion of the United States and world energy production could be supplied by LFFH plants. The LFFH engine described utilizes a central fusion chamber surrounded by multiple layers of multiplying and moderating media. These layers, or blankets, include coolant plenums, a beryllium (Be) multiplier layer, a fertile fission blanket and a graphite-pebble reflector. Each layer is separated by perforated oxide dispersion strengthened (ODS) ferritic steel walls. The central fusion chamber is surrounded by an ODS ferritic steel first wall. The first wall is coated with 250-500 {micro}m of tungsten to mitigate x-ray damage. The first wall is cooled by Li{sub 17}Pb{sub 83} eutectic, chosen for its neutron multiplication and good heat transfer properties. The {sub 17}Pb{sub 83} flows in a jacket around the first wall to an extraction plenum. The main coolant injection plenum is immediately behind the Li{sub …