Considering the strong built-in electric field(BEF) in the wurtzite cylindrical GaN quantum dot(QD) with finite potential barriers, the interband optical transitions due to the exciton bound by an ion with charge －e (called ionized acceptor bound exciton (A-, X)) are investigated theoretically by means of the variational method. Numerical results show that the emission wavelengths sensitively depend on the QD size(L and R), the position of the ionized acceptor and Al composition x of the barrier material Alx Ga1-x N. The transition wavelength increases if the QD height, QD radius and Al composition x are increased. The emission wavelength firstly increases when the ionized accptor is moved from the left barrier of the QD to right along z-direction, and reaches its maximum when the acceptor is in the vicinity of the left interface of QD. Then the transition wavelength decreases if the acceptor is continuously moved toward right. The minimum value of the transition wavelength can be obtained when the acceptor is in the vicinity of the right interface of QD. The wavelength increases again if the acceptor is further moved to the right barrier of QD. The emission wavelength increases when the acceptor position ρ0 goes from the center of QD. Comparing with the free exciton state without the acceptor, the emission wavelength increases with introducing the ionized acceptor impurity into the left side of the QD center, and the emission wavelength reduces with introducing the ionized acceptor impurity into the right side of the QD center.