The local power density should be estimated accurately to prevent fuel rod melting. The local power density at the hottest part of a hot fuel rod, which is described by the power peaking factor, is more important information than the local power density at any other position in a reactor core. Therefore, in this work, the power peaking factor, which is defined as the highest local power density to the average power density in a reactor core, is estimated by fuzzy neural networks using numerous measured signals of the reactor coolant system. The fuzzy neural networks are trained using a training data set and are verified with another test data set. They are then applied to the first fuel cycle of Yonggwang nuclear power plant unit 3. The estimation accuracy of the power peaking factor is 0.45% based on the relative $2_{sigma}$ error by using the fuzzy neural networks without the in-core neutron flux sensors signals input. A value of 0.23% is obtained with the in-core neutron flux sensors signals, which is sufficiently accurate for use in local power density monitoring.