We introduce a novel dependent type theory called Graded Modal Dependent Type Theory (GrTT) that provides a new solution to the long-standing challenge of how to combine linear logic and dependent types. The key to reconciling these two notions is to leverage the recent approach of graded types, which treats data as a resource which is subject to fine-grained, quantitative tracking in the type system. GrTT offers fine-grained control over resource usage at both the runtime value level and the type level. We argue that the combination of linearity, graded modalities, and dependent types provides a rich language for specifying and reasoning about dependently-typed programs in a more fine-grained way than current approaches, enabling precise reasoning about usage information on compound data in a dependently-typed setting.