The aim of this work is to develop a single anti-spoofing system which can be applied to effectively detect all the types of spoofing attacks considered in the ASVspoof 2019 Challenge: text-to-speech, voice conversion and replay based attacks. To achieve this, we propose the use of a Light Convolutional Gated Recurrent Neural Network (LC-GRNN) as a deep feature extractor to robustly represent speech signals as utterance-level embeddings, which are later used by a back-end recognizer which performs the final genuine/spoofed classification. This novel architecture combines the ability of light convolutional layers for extracting discriminative features at frame level with the capacity of gated recurrent unit based RNNs for learning long-term dependencies of the subsequent deep features. The proposed system has been presented as a contribution to the ASVspoof 2019 Challenge, and the results show a significant improvement in comparison with the baseline systems. Moreover, experiments were also carried out on the ASVspoof 2015 and 2017 corpora, and the results indicate that our proposal clearly outperforms other popular methods recently proposed and other similar deep feature based systems.