In recent years, artificial neural networks (ANNs) have been commonly used for time series forecasting by researchers from various fields. There are some types of ANNs and feed forward neural networks model is one of them. This type has been used to forecast various types of time series in many implementations. In this study, a novel multiplicative seasonal ANN model is proposed to improve forecasting accuracy when time series with both trend and seasonal patterns is forecasted. This neural networks model suggested in this study is the first model proposed in the literature to model time series which contain both trend and seasonal variations. In the proposed approach, the defined neural network model is trained by particle swarm optimization. In the training process, local minimum traps are avoided by using this population based heuristic optimization method. The performance of the proposed approach is examined by using two real seasonal time series. The forecasts obtained from the proposed method are compared to those obtained from other forecasting techniques available in the literature. It is seen that the proposed forecasting model provides high forecasting accuracy.