Motivation: Proteins are ubiquitous molecules whose function in biological processes is determined by their 3D structure. Experimental identification of a protein's structure can be time-consuming, prohibitively expensive and not always possible. Alternatively, protein folding can be modeled using computational methods, which however are not guaranteed to always produce optimal results. GraphQA is a graph-based method to estimate the quality of protein models, that possesses favorable properties such as representation learning, explicit modeling of both sequential and 3D structure, geometric invariance and computational efficiency. Results: GraphQA performs similarly to state-of-the-art methods despite using a relatively low number of input features. In addition, the graph network structure provides an improvement over the architecture used in ProQ4 operating on the same input features. Finally, the individual contributions of GraphQA components are carefully evaluated. Availability and implementation: PyTorch implementation, datasets, experiments and link to an evaluation server are available through this GitHub repository: github.com/baldassarreFe/graphqa. Supplementary information: Supplementary data are available at Bioinformatics online.