The weak-localization of the two-dimensional electron gas (2DEG) in a modulation-doped Al0.22Ga0.78N/GaN single quantum well has been investigated through the magnetoresistance measurements. The elastic scattering time tau(epsilon), dephasing time tau(phi) and spin-orbit(s-o) scattering time tau(so) at various temperatures are obtained. The fitting parameters indicate that the inelastic scatterings to the 2DEG are mainly due to the piezoelectric field and the alloy disorder in the AlxGal-xN barrier. When the second subband in the triangular quantum well at the heterointerface is occupied by the 2DEG, the anti-weak localization is observed clearly, which is due to the strong spin-orbit interaction. The spin-orbit effect dominates the quantum correction of the conductivity in the upper subband. The intersubband scattering becomes stronger with increasing temperature.