In this paper, the problem of exponential stability for discrete-time switched genetic regulatory networks (GRNs) with persistent dwell-time (PDT) switching and time delays is concerned. The novelty of this paper is derived from introducing an extended property of quadratic convex function, and utilizing an improved summation inequality together with an extended reciprocally convex matrix inequality, which is less conservative than the Jensen inequality and the reciprocally convex combination employed in the discrete-time delay systems. In addition, the considered switching regularity is more general than dwell-time (DT) switching and average dwell-time (ADT) switching. Moreover, by introducing the delay partitioning method and the piecewise Lyapunov–Krasovskii functional, a set of sufficient conditions are established in the form of linear matrix inequalities to guarantee the discrete-time PDT switched GRNs with constant time delays and time-varying delays are exponentially stable, respectively. Finally, some numerical examples are exploited to demonstrate the validity and potential of the proposed method.