A one-dimensional discrete chaotic system is constructed based on the hybrid architecture of single-electron transistor and metal oxide semiconductor in this paper. Voltage transfer characteristics of the parallel architecture of single-electron transistor and metal oxide semiconductor are investigated, and the corresponding N-shape piecewise linear function model is established. Based on this model a one-dimensional discrete mapping system is first constructed, the dynamics of the system is then analyzed including one-dimensional mapping process, bifurcation diagram and Lyapunov exponent spectrum and the corresponding discrete chaotic system is finally designed through the electronic circuits of the hybrid architecture. The simulation result is consistent with the theoretical analysis. All these indicate that discrete chaotic system designed by the hybrid architecture of single-electron transistor and metal oxide semiconductor has some advantages such as simple circuit structure and low power dissipation, which are good for the integration and application of chaotic system.