A recently proposed, novel approach to inertial confinement fusion is examined as a potential source of fast neutrons. Known as the magnetically insulated inertial confinement fusion (MICF) system, it combines the favorable aspects of both magnetic and inertial fusions into one. In this approach, the hot fusion plasma is created inside a hollow spherical pellet whose inner walls are coated with deuterium-tritium fuel and ablated by a laser that enters the target through a hole. Physical containment of the plasma is provided by the metallic shell that surrounds the fuel, while its thermal energy is insulated from the wall by a strong, self-generated magnetic field. In contrast to implosion-type inertial fusion systems, the lifetime of the hot plasma in MICF is dictated by the shock speed in the shell, rather than by the sound speed in the plasma; as a result, it is about two orders of magnitude longer. This translates into a significantly higher Q (ratio of fusion energy to input energy) values at modest input laser energies, which in turn means it can serve as an effective source of high energy neutrons.