The structural and electronic properties of ZnO (10 (1) over bar0) and (11 (2) over bar0) surfaces were investigated by means of density functional theory applied to periodic calculations at B3LYP level. The stability and relaxation effects for both surfaces were analyzed. The electronic and energy band properties were discussed on the basis of band structure as well as density of states. There is a significant relaxation in the (10 (1) over bar0) as compared to the (11 (2) over bar0) terminated surfaces. The calculated direct gap is 3.09, 2.85, and 3.09 eV for bulk, (10 (1) over bar0), and (11 (2) over bar0) surfaces, respectively. The band structures for both surfaces are very similar.