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Weather Data Mining is a form of Data mining concerned with finding hidden patterns inside largely available meteorological data, so that the information retrieved can be transformed into usable knowledge. A variety of data mining tools and techniques are available in the industry, but they have been used in a very limited way for meteorological data. In this paper, a neural network-based algorithm for predicting the atmosphere for a future time and a given location is presented. We have used Back Propagation Neural (BPN) Network for initial modelling. The results obtained by BPN model are fed to a Hopfield Network. The performance of our proposed ANN-based method (BPN and Hopfield Network based combined approach) tested on 3 years weather data set comprising 15000 records containing attributes like temperature, humidity and wind speed. The prediction error is found to be very less and the learning converges very sharply. The main focus of this paper is based on predictive data mining by which we can extract interesting (non-trivial, implicit, previously unknown and potentially useful) patterns or knowledge from huge amount of meteorological data.