A new fast-running analytic model has been developed for analyzing the load follow operation. The new model was based on the neural network theory, which has the capability of modeling the input/output relationships of a nonlinear system. The new model is made up of two error back-propagation neural networks and procedures to calculate core parameters, such as the distributions and density of xenon in a quasi-steady-state core like load follow operation. One neural network is designed to retrieve the axial offset of power distribution, and the other is for reactivity corresponding to a given core condition. The training data sets for learning the neural networks in the new model are generated with a three-dimensional nodal code and, also, the measured data of the first-day test of load follow operation. Using the new model, the simulation results of the 5-day load follow test in a pressurized water reactor show a good agreement between the simulation data and the actual measured data. Required computing time for simulating a load follow operation is comparable to that of a fast-running lumped model. Moreover, the new model does not require additional engineering factors to compensate for the difference between the actual measurements and analysis results because the neural network has the inherent learning capability of neural networks to new situations.