By LLP(Lee-Low-Pines)-like transformation and fractional-dimension variational treatment, the ground-state energies of excitons confined in Ga1－xAlxAs/GaAs/Ga0.7Al0.3As asymmetric square quantum well and the influence of phonons are demonstrated. The exciton ground-state energy has a minimum value with the increasing well width. And we make clear the effects of the barrier height on the fractional dimension, exciton ground energy and binding energy. After taking into account of the interaction of exciton with LO-phonons, the values of the exciton ground-state energies increase remarkablely. Moreover, the exciton binding energy increases as the asymmetric well-width decreases or the barrier height increases.