This research demonstrates the physical feasibility of constructing a single degree of freedom ocean-wave energy capturing device of extremely high efficiency, which serves also as an almost-perfect floating breakwater. The device consists of an asymmetric heaving floater and a power-take-off (PTO) system. A special geometry was first designed to have minimal effects from viscosity. As such, potential-flow analysis proved adequate for predicting the behavior of the device even in a real-fluid environment. Per ideal-fluid theory, at the heave resonance frequency, when the absorption damping of the PTO is matched with the radiation damping of the floater, an energy extraction efficiency of 96.34% can be achieved. At this high-efficiency condition, the transmitted waves beyond the floater are 12.5% of the incident-wave amplitude (or a mere 1.56% of the incident-wave energy). A working two-dimensional physical unit of 0.227 m beam and 0.8m draft was designed and fabricated to work with the permanent magnet linear generator developed in (Yeung et al., 2012). The floater-PTO system was tested at The Model-Testing Facility of the University of California (UC), Berkeley. Experiments showed that when the PTO operates at even just 48% of the optimal damping, the device yields already an energy-capturing efficiency of 82%, with only 2% of the incident-wave energy transmitted. These latter values are in agreement with the theoretical predictions. Restraining lateral force and pitching moment are shown, as well as how wave energy is directed to the PTO.