This paper examines the size effect in quasi-brittle materials using a three-dimensional bond-based peridynamic model. This is the first time that the capability of a peridynamic model to capture the size effect in quasi-brittle materials has been examined. Correctly reproducing the size effect is an essential check on the validity of any computational model and it is demonstrated that a bond-based peridynamic model can accurately capture the failure stress of geometrically identical structures over a range of sizes. A systematic examination of geometrically similar notched and unnotched beams provides new insights into the predictive capabilities of the model, and mode I and mixed-mode problems are considered to examine the generality of the model. The model is validated using published experimental data, and the predictive accuracy is equivalent, if not superior, to well-established numerical methods whilst offering several benefits that justify further research and development. This study provides evidence that the length scale in a peridynamic model is a numerical parameter and not a material property.