A new method of realizing a discrete chaotic system using the hybrid architecture of single-electron transistor (SET) and metal oxide semiconductor (MOS) is proposed in this paper. The transfer characteristic for two parallel SETs with a biased current source is investigated and the corresponding S-shape piecewise linear function model is established. Based on this model a one-dimensional discrete mapping system is first constructed, and the dynamics of the system is then analyzed through one-dimensional mapping process bifurcation diagram and Lyapunov exponents, and the corresponding discrete chaotic system is finally designed through the electronic circuit of SET-MOS hybrid architecture. All these indicate that our approach not only is feasible but also has some advantages such as simple circuit structure and good integration compared with existing methods.