The two most commonly used types of artificial neural networks (ANNs) are the multilayer feed-forward and multiplicative neuron model ANNs. In the literature, although there is a robust learning algorithm for the former, there is no such algorithm for the latter. Because of its multiplicative structure, the performance of multiplicative neuron model ANNs is affected negatively when the dataset has outliers. On this issue, a robust learning algorithm for the multiplicative neuron model ANNs is proposed that uses Huber's loss function as fitness function. The training of the multiplicative neuron model is performed using particle swarm optimization. One principle advantage of this algorithm is that the parameter of the scale estimator, which is an important factor affecting the value of Huber's loss function, is also estimated with the proposed algorithm. To evaluate the performance of the proposed method, it is applied to two well-known real world time series datasets, and also a simulation study is performed. The algorithm has superior performance both when it is applied to real world time series datasets and the simulation study when compared with other ANNs reported in the literature. Another of its advantages is that, for datasets with outliers, the results are very close to the results obtained from the original datasets. In other words, we demonstrate that the algorithm is unaffected by outliers and has a robust structure.