Predicting the next activity of a running execution trace of a business process represents a challenging task in process mining. The problem has been already tackled by using different machine learning approaches. Among them, deep artificial neural networks architectures suited for sequential data, such as recurrent neural networks (RNNs), recently achieved the state of the art results. However, convolutional neural networks (CNNs) architectures can outperform RNNs on tasks for sequence modeling, such as machine translation. In this paper we investigate the use of stacked inception CNN modules for the next-activity prediction problem. The proposed neural network architecture leads to better results when compared to RNNs architectures both in terms of computational efficiency and prediction accuracy on different real-world datasets.