In 1971, memristor theory was proposed and described by Leon Chua. But first practical implementation has been realized by a group of researchers from Hewlett-Packard laboratories in 2008. Memristor has drawn the worldwide attention after this innovation. This work introduces a new CMOS based memristor realization employing DDCC (Differential Difference Current Conveyor) based circuit blocks which are easy for VLSI implementation. Simulation results show that the realization proposed satisfies memristor properties and it can be well applied to chaotic secure communication circuits.