The magnetic nanowires have attracted great interests recently for their potential applications in novel logic and memory devices [1,2]. The magnetization reversal of the magnetic nanowires is realized by the nucleation and the propagation of domain walls (DWs) along the wires. Both current and magnetic field driven DW motion have been proposed and investigated widely. One of the techniques to manipulate the DW is to introduce artificial defects to the nanowire structure such as different shapes of notches. Asymmetric notches have been reported to act as an asymmetric energy barrier for the DW and the depinning field and critical depin current depend on the direction of DW propagation, which is related to the slope of notch[3-5]. The "Magnetic ratchet effect"  has been addressed since the DW depins and moves easier in one direction than the other. Magnetic diodes were also proposed based on the asymmetric notch structure in magnetic nanowires . However, rather than constriction, the previous reports [3-7] were based on the protruding shape of asymmetric notch. In this paper, we present a study on the depinning behaviour of the DW inside magnetic nanowires with a single inward asymmetric notch.