Magnetic Resonance Imaging (MRI) has evolved as a clinical standard-of-care imaging modality for cardiac morphology, function assessment, and guidance of cardiac interventions. All these applications rely on accurate extraction of the myocardial tissue and blood pool from the imaging data. Here we propose a framework for left ventricle (LV) segmentation from cardiac cine-MRI. First, we segment the LV blood pool using iterative graph cuts, and subsequently use this information to segment the myocardium. We formulate the segmentation procedure as an energy minimization problem in a graph subject to the shape prior obtained by label propagation from an average atlas using affine registration. The proposed framework has been validated on 30 patient cardiac cine-MRI datasets available through the STACOM LV segmentation challenge and yielded fast, robust, and accurate segmentation results.