Different diseases can affect an individual's gait in different ways and, therefore, gait analysis can provide important insights into an individual's health and well-being. Currently, most systems that perform gait analysis using 2D video are limited to simple binary classification of gait as being either normal or impaired. While some systems do perform gait classification across different pathologies, the reported results still have a considerable margin for improvement. This paper presents a novel system that performs classification of gait across different pathologies, with considerably improved results. The system computes the walking individual's silhouettes, which are computed from a 2D video sequence, and combines them into a representation known as the gait energy image (GEI), which provides robustness against silhouette segmentation errors. In this work, instead of using a set of handcrafted gait features, feature extraction is done using the VGG-19 convolutional neural network. The network is fine-tuned to automatically extract the features that best represent gait pathologies, using transfer learning. The use of transfer learning improves the classification accuracy while avoiding the need of a very large training set, as the network is pre-trained for generic image description, which also contributes to a better generalization when tested across different datasets. The proposed system performs the final classification using linear discriminant analysis (LDA). Obtained results show that the proposed system outperforms the state-of-the-art, achieving a classification accuracy of 95% on a dataset containing gait sequences affected by diplegia, hemiplegia, neuropathy and Parkinson's disease, along with normal gait sequences.