Dense granular materials display a complicated set of flow properties, which differentiate them from ordinary fluids. Despite their ubiquity, no model has been developed that captures or predicts the complexities of granular flow, posing an obstacle in industrial and geophysical applications. Here we propose a 3D constitutive model for well-developed, dense granular flows aimed at filling this need. The key ingredient of the theory is a grain-size-dependent nonlocal rheology—inspired by efforts for emulsions—in which flow at a point is affected by the local stress as well as the flow in neighboring material. The microscopic physical basis for this approach borrows from recent principles in soft glassy rheology. The size-dependence is captured using a single material parameter, and the resulting model is able to quantitatively describe dense granular flows in an array of different geometries. Of particular importance, it passes the stringent test of capturing all aspects of the highly nontrivial flows observed in split-bottom cells—a geometry that has resisted modeling efforts for nearly a decade. A key benefit of the model is its simple-to-implement and highly predictive final form, as needed for many real-world applications.