Asymptotic tracking control of uncertain nonlinear system with input quantization is an important, yet challenging issue in the field of adaptive control. So far, there is still no result available in addressing this issue even for the case of time-invariant reference signal. In this paper, we solve this problem by proposing a new tuning function control scheme which is designed on the basis of a novel decomposition of hysteresis quantizer. It is proved that the proposed scheme ensures the global boundedness of all closed-loop signals and the asymptotic convergence of tracking error to zero. Moreover, an explicit bound for the L-norm of the tracking error is derived, which shows that the transient performance can also be improved with the proposed scheme.