Hybrid CMOS-SET architectures, which combine the merits of CMOS and single electron transistor (SET) devices, promise to be a practical implementation for nanometer scale circuit design. In this work, we propose the design of two typical arithmetic circuits, namely adder and multiplier, using hybrid CMOS-SET architectures. For full adders (FAs) design, we present three different implementations based on multiple-valued logic (MVL), phase modulation and frequency modulation. These FAs fully utilize SET's unique characteristic of Coulomb blockade oscillation and exhibit improved performance in terms of circuit area/complexity, power dissipation and temperature effect. The structure based on frequency modulation also possesses high immunity against background charges, and is extended to design of multiple-bit adder and multiplier.