A wave power extraction system is under development at the Port and Harbour Research Institute. The extractor is a pneumatic type wave power convertor to be fitted to a vertical breakwater. The turbine invented by Wells is selected as the air turbine of the present extracting system. The turbine can produce rotational power of uni-direction without a valve system even when the air flow reverses its direction. An explicit theory without any empirical parameters was derived to predict the conversion from wave power to air power. The theory is extended to include the turbine and generator system utilizing the characteristics of the Wells turbine. The thoery is well confirmed by a series of model experiments using regular and irregular waves. The theory and the experimental results as well as the design procedure of the turbine are presented in this report.