Diffusion tensor imaging (DTI) is a Magnetic Resonance Imaging (MRI) technique that can reveal in vivo tissue microstructure by measuring diffusion of water in tissue. DTI has become an important tool in many clinical applications, such as assessment of white matter maturation, locating white matter lesions, and providing anatomical connectivity information. However, DTI usually requires long examination times due to the repetitive nature of the acquisition and is very sensitive to motion. These drawbacks have become the largest obstacles to full utilization of DTI. In this work, we propose to overcome these obstacles by using a model-based compressive imaging approach. Our approach consist of models to efficiently represent diffusion-encoded images and the corresponding recovery schemes based on compressive sensing (CS) principles. Our results indicate that the proposed model-based approach can allow reliable recovery of DTI signal from undersampled measurements and outperforms conventional CS recovery.