Hydrodynamic performance and power absorption of an oscillating buoy wave energy converter (WEC) with 3 degrees of freedom (DOFs) are studied. The DOFs are surge, heave and pitch. Linear potential theory is utilized. Optimal PTO damping coefficient is selected. Optimal PTO power output and capture width ratios are calculated and compared. Influences of the buoy's radius, draft and geometry are investigated. The geometries are cylinder, hemisphere-bottom cylinder, cone-bottom cylinder, linear-chamfered cylinder and circular-chamfered cylinder. Results show that only surge and pitch interact with each other. The interaction is intensified on the resonant frequency of pitch, and is significant with special radius and draft. Power absorption of 3-DOF WEC increases significantly (at least 46.6% here) than unidirectional WEC and the power absorption band is wider. Heave is the main power capture DOF. Pitch gets the biggest power absorption at the resonant wave frequency. Increasing radius benefits the power capture efficiency at low wave frequencies and is harmful at high wave frequencies, except for pitch motion. Increasing draft benefits the power capture efficiency in surge and heave, but is harmful in pitch. For surge, heave and 3-DOF motion, cylinder is the best shape. For pitch, the hemisphere is the best shape.