Heart failure is a major health concern and is the leading cause of hospitalization among elderly Americans. Currently 5.7 million Americans are estimated to have heart failure and the estimated direct and indirect costs of treating heart failure are approximately $37.2 billion. Approximately 40% of those diagnosed with heart failure will have heart failure with preserved ejection fraction (HFPEF). These individuals have significant restrictions in their ability to carry out activities of daily living. Exercise training has been established as adjuvant therapy in heart failure. Although exercise training guidelines for treatment of heart failure with reduced ejection fraction (HFREF) are well established, no consensus exercise guidelines exist for management of HFPEF. Aerobic and cardiovascular adaptations are generally greater after high-intensity exercise training; interval-type exercise facilitates this type of training because it allows for rest periods that make it possible for patients with heart failure to perform short (e.g., 1-4 minutes) work periods at intensities that are higher than would be possible during continuous exercise. High-intensity aerobic interval training presents a unique, yet untested, therapeutic modality for the exercise training of patients with heart failure with preserved ejection fraction. Pilot testing is warranted, results of which may have important implications for reducing cardiovascular risk, increasing short- and long-term quality of life and survival, and reducing healthcare costs in this patient population. The investigators primary specific aim is to determine the efficacy of a novel, high-intensity aerobic interval exercise training program for improving VO2peak (peak oxygen uptake), endothelial function, and arterial stiffness in patients with HFPEF. The investigators secondary aim is to determine whether the vascular changes are correlated with the changes in VO2peak.