Integrating oscillating-water-column type converters (pneumatic chambers) with slack-moored floating breakwaters can be a viable option for cost-sharing between wave energy capturing devices and shore-protection structures, and thus enhance the cost-effectiveness of wave energy utilization. When designing such integrated systems, it is desirable to have a system that can capture wave energy over a wide range of wave frequency. In this study, a configuration of floating breakwater with asymmetric pneumatic chambers (a narrower chamber on the seaside and a wider chamber on the leeside) is proposed to increase the amplitude of the oscillating air-pressures inside both chambers over a wide range of wave frequency (thus to improve the performance in wave energy extraction). A series of experiments were carried out under regular wave conditions to study the effects of asymmetric pneumatic chambers on the hydrodynamic performance of the floating breakwater and on the oscillating air-pressures inside the two chambers. It was shown that (1) the breakwater with asymmetric chambers performed as good as that with symmetric chambers in terms of wave transmission and motion responses and (2) with asymmetric configuration, it is possible to increase the amplitude of the oscillating air-pressures inside both chambers. The new concept provides a promising way to extend the frequency range over which wave energy can be extracted.