Deep learning has been recently applied as an alternative method for several choice problems, such as mode choice. Nevertheless, this method has not been particularly explored for route choice, despite its possible advantages. This work proposes a novel model for predicting route choice in public transport based on a convolutional neural network. The model has several advantages compared to the state of the art (e.g., Path Size Logit model). First, the model can infer a nonlinear utility function for the available routes. Second, it can also easily include any non-alternative-specific variable, such as socioeconomic characteristics or weather conditions, allowing complex interactions with all other variables. Third, the model generalizes the Path Size Logit, and thus can obtain the same or better performance. The model is tested on a large-scale study based on GPS tracking, observing more than 2700 public transport trips of Zurich residents. The model is tested also on a synthetic dataset, to study its properties, performance, and ability to describe different utility functions. Finally, the performances of the model are compared with the state of the art.