In a self-rectifying air turbine for wave energy conversion, it is reported that the rotor encountered different maximum velocities between the inhalation and exhalation processes of the oscillating water column. This paper describes the development of an efficient turbine suitable for such actual asymmetric flow conditions. The air turbine with staggered blades has been presented and investigated experimentally by model testing under steady flow conditions. The running and starting characteristics under pseudo-sinusoidal oscillating flow conditions were then clarified by using a quasi-steady analysis. As a result, it is found that the air turbine with staggered blades is superior to the Wells turbine, and a suitable choice of design factor has been suggested for the preset angle of the rotor.