The electronic properties of a (10 (1) over bar 0)-oriented wurtzite (WZ) GaN/AlGaN quantum well (QW) are investigated using the multiband effective-mass theory. These results are compared with those of a (0001)-oriented WZ GaN/AlGaN QW with the piezoelectric (PZ) effect taken into account. For the (0001)-oriented structure, the optical matrix element is significantly reduced with increasing the well thickness due to the PZ electric field. This means that, in the (0001)-oriented structure, a QW structure with a thinner well thickness is desirable to obtain better laser characteristics. For the (10 (1) over bar 0)-oriented structure, it is found that the average hole effective masses are largely reduced compared to those for the (0001)-oriented structure. Also, the (10 (1) over bar 0)-oriented structure shows a much larger optical matrix element for y'-polarization due to the crystal orientation effect. These results suggest that the (10 (1) over bar 0)-oriented QW structures show improved characteristics compared to the (0001)-oriented QW structure with the PZ effect.