First-pass perfusion cardiac magnetic resonance (FPP-CMR) allows the assessment of coronary heart disease. However, conventional FPP-CMR suffers from low spatial resolution, insufficient heart coverage and requires long breath-holds. At present, perfusion abnormalities are usually identified visually by highly trained physicians. Recently, quantitative analysis of FPP-CMR has emerged as a more reliable and operator-independent approach for identifying perfusion defects. Typically, quantitative FPP-CMR first reconstructs individual dynamic images, which are then converted to contrast agent concentration, and finally, tracer-kinetic modeling is used to generate quantitative myocardial perfusion maps. Here, we propose a model-based FPP-CMR reconstruction approach, which combines image reconstruction and tracer-kinetic modeling, to better exploit the redundancies in the FPP-CMR data. We show that such synergistic approach enables very high undersampling rates at each time frame, and thus allows for much higher spatial resolution and coverage than the traditional method. Furthermore, our proposed method can be combined with respiratory motion correction and k-t undersampling to improve myocardial perfusion quantification, while substantially increasing patient comfort.