The memristor, which has the features of frequency hysteresis quality, easy controlled memristance and so on, is considered as the fourth fundamental two terminal circuit component besides the resistor, capacitor and inductor. This paper deduces the initial state related frequency characteristic of memristor on the theory and verifies that on the numerical simulation, where the memristor is a passive metal oxide metal (Pt TiO2 Pt) device fabricated by 〖HJ*4/9〗HP Labs. Meanwhile, a digital controlled and memristor based self adaptive filter circuit has been designed in terms of the characteristic. The circuit can realize frequency selecting via changing the initial memristance and then changing the cut off frequency.