Aortic stenosis has been thought to be a degenerative process basically induced by long-lasting mechanical stress, and hemodynamic factors such as shear forces, acceleration of blood flow, hypertension and rapid heart rate might contribute to progression of aortic stenosis. Peak aortic jet velocity is known to be associated with clinical outcomes in mild and moderate AS, and our previous study showed that rate of progression was significantly associated with baseline aortic jet velocity in mild aortic stenosis. Because beta-blocker therapy would decrease aortic jet velocity and heart rate, it might decrease hemodynamic stress and eventually slow down the degenerative process in patients whose disease is not too advanced for therapy to be effective. The investigators hypothesized that a beta-blocker therapy would decrease the rate of progression of aortic stenosis by modifying hemodynamic factors favorably in patients with mild to moderate aortic stenosis.