Boiling water reactors (BWRs) represent a large fraction of the world's installed nuclear power capacity. The core model of a BWR is very complex because it has many fuel assemblies and strong axial heterogeneities such as coolant voiding, partial control rod insertion, and non-uniform fuel assembly design. In order to operate a BWR safely, it is necessary to supervise the performance of the reactor core during the operation cycle. Therefore, the operation of the reactor core in a BWR is supervised using a 3-dimensional on-line simulator. In order to raise the calculation accuracy of this 3-dimensional simulator, the calculation power distribution is corrected using the neutron flux distribution obtained by the in-core instrumentation. In this paper, a model that uses a neural network was developed in order to raise the calculation accuracy of this 3-dimensional simulator further. In order to apply a neural network to the complicated reactor core of a BWR, the learning algorithm needs to be improved. Therefore, a technique using the Quasi-Newton method for renewal of the connection weights of the Back-Propagation (BP) method was developed. Using this algorithm, the convergent ability of neural network learning was improved in the strongly nonlinear problems. When this algorithm was applied to a BWR, the calculation accuracy of a 3-dimensional simulator was improved considerably.