Adaptive control of discrete-time parametric-strict-feedback nonlinear systems will be studied in this paper. To the best knowledge of the authors, almost all of the existing results for such systems need Lipschitz condition. The main purpose of this paper is to take a step towards nonlinear growth rate for second-order systems. The control law is designed based on least squares (LS) algorithms and on recursive adaptive predictors. Global stability and tracking performance are established for the closed-loop systems. Adaptive control of discrete-time parametric-strict-feedback nonlinear systems will be studied in this paper. To the best knowledge of the authors, almost all of the existing results for such systems need Lipschitz condition. The main purpose of this paper is to take The control law is designed based on least squares (LS) algorithms and on recursive adaptive predictors. Global stability and tracking performance are established for the closed-loop systems.