The risk of forest fire occurrence is affected by the interactions among forest fuels, weather, human activities, etc. In the present paper, we try to build a method to model and forecast forest fire risk based on artificial neural networks. The data considered include population density and several weather parameters, i.e. average relative humidity, wind velocity and daily sunshine hours. With an interpolation method, these data have been expanded into 1 by 1 km meshes that are calculated according to the standard mesh code system in Japan, where the Japanese territory is divided into a lattice by latitude and longitude. Different parameter combinations and corresponding fire probabilities are computed. The correlations between forest fire probability and population density, and sequentially that between forest fire probability and combinations of population density together with one or several weather parameters are analyzed with three back-propagation neural networks in comparison with polynomial regression investigations. The results indicate that non-linear relationships exist among the influential factors and forest fire probability; artificial neural networks could better capture the non-linearity and give closer results to the test set compared with polynomial regression. The proposed method may be used to investigate and forecast forest fire risk providing there are enough data.