One of the main challenges in drug discovery is to find molecules that bind specifically and strongly to their target protein while having minimal binding to other proteins. By predicting binding affinity, it is possible to identify the most promising candidates from a large pool of potential compounds, reducing the number of compounds that need to be tested experimentally. Recently, deep learning methods have shown superior performance than traditional computational methods for making accurate predictions on large datasets. However, the complexity and time-consuming nature of these methods have limited their usage and development. Quantum machine learning is an emerging technology that has the potential to improve many classical machine learning algorithms. In this work we present a hybrid quantum-classical convolutional neural network, which is able to reduce by 20% the complexity of the classical network while maintaining optimal performance in the predictions. Additionally, it results in a significant time savings of up to 40% in the training process, which means a meaningful speed up of the drug discovery process.