This paper deals with the adaptive control of linearly parameterized discrete-time nonlinear system in the presence of bounded disturbances and unmodeled dynamics. A new adaptive law is presented. No a priori knowledge about the bounds on both the plant parameters and unmodeled uncertainty is required to implement the estimation algorithm. The adaptive scheme is free from singularity. This is achieved through the use of some time-varying adaptation gain. It is established that if the plant model nonlinearity is sector-bounded then the BIBO stability of the closed-loop system will be guaranteed. Simulation results are given to demonstrate the performance of the adaptive controller.