A core of a light water reactor has a plurality of fuel assemblies. The fuel assemblies include a plurality of fuel rods in which a lower end is supported by a lower tie-plate and an upper end is supported by an upper tie-plate. The fuel rods form plenums above a nuclear fuel material zone and have a neutron absorbing material filling zone under the nuclear fuel material zone. Neutron absorbing members attached to the upper tie-plate are disposed between mutual plenums of the neighboring fuel rods above the nuclear fuel material zone. The neutron absorbing members have a length of 500 mm and are positioned at a distance of 300 mm from the nuclear fuel material zone. Even if the overall core is assumed to become a state of 100% void, no positive reactivity is inserted to the core.