In this paper, we will study adaptive control of a class of discrete-time parametric-strict-feedback non-linear stochastic systems. Almost all the existing results for such systems need Lipschitz condition. The main purpose of this paper is to remove this restriction and to get some positive result under non-linear growth condition. The control law is designed based on weighted-least-squares (WLS) algorithms and on recursive adaptive predictors. Global stability and tracking performance are established for the closed-loop systems.