Memristor is a passive two terminal electronic device that maintains a functional relationship between the time integrals of current and voltage. Memristor theory was proposed and described by Leon Chua in 1971. But the first practical implementation has been realized by Williams' group at HP laboratory in 2008. Memristor has drawn the worldwide attention after HP released its invention. This paper discusses the memristor and proposes a new CMOS memristor model. The model is very suitable especially chaotic communication circuits. Performance of the model is proved via simulations.