This paper considers the stability problem of discrete-time switched linear systems in the presence of parametric uncertainties. Parametric uncertainty is sometimes called structured uncertainty because of the structure of the model is known, but some of the parameters are uncertain. From the practical viewpoint, it is important to investigate the robust stability conditions of uncertain switched systems. Therefore, under the assumption of knowing the structure of the uncertainty matrix and based on the common Lyapunov function for the nominal switched system, sufficient conditions for robust exponential stability of the discrete-time uncertain switched system (under any switching signal) are derived. Sufficient conditions are formulated in terms of matrix inequalities for fixed values of some parameters which may be solved via LMI techniques based on numerical methods. Moreover, a procedure is proposed to determine the maximum admissible bounds of the uncertain parameters which characterize the exponential stability of the uncertain switched system. Finally, numerical examples are provided to verify the theoretical results.