Aimed at the problems that existing discrete-time prescribed performance control (PPC) methodology is high in dependence on sliding mode reaching laws and obvious in chattering defects, a new discrete time PPC approach is proposed for a seeker's stability platform by constructing a new design framework without using sliding mode control. Firstly, the discrete time performance functions are developed to impose envelope constraints on tracking errors. And then, a discrete time transformed error is defined to construct a novel feedback function. Furthermore, discrete time PPC protocols are explored to stabilize the newly developed feedback function instead of the transformed error, guaranteeing not only all the tracking errors with desired prescribed performance, and remedying the defects of control chattering caused by the dependence of control algorithms on sliding mode reaching laws. Finally, by comparing the simulation results and verifying, the method is valid and superior.