Protein tertiary structure prediction methods have matured in recent years. However, some proteins defy accurate prediction due to factors such as inadequate template structures. While existing model quality assessment methods predict global model quality relatively well, there is substantial room for improvement in local quality assessment, i.e. assessment of the error at each residue position in a model. Local quality is a very important information for practical applications of structure models such as interpreting/designing site-directed mutagenesis of proteins. We have developed a novel local quality assessment method for protein tertiary structure models. The method, named Graph-based Model Quality assessment method (GMQ), explicitly considers the predicted quality of spatially neighboring residues using a graph representation of a query protein structure model. GMQ uses conditional random field as its core of the algorithm, and performs a binary prediction of the quality of each residue in a model, indicating if a residue position is likely to be within an error cutoff or not. The accuracy of GMQ was improved by considering larger graphs to include quality information of more surrounding residues. Moreover, we found that using different edge weights in graphs reflecting different secondary structures further improves the accuracy. GMQ showed competitive performance on a benchmark for quality assessment of structure models from the Critical Assessment of Techniques for Protein Structure Prediction (CASP).