A novel dynamic spatially selective dephasing (DSSD) for outer volume suppression (OVS) is introduced. This technique uses high-order shim pulses to accomplish OVS by creating a low and high field gradient within and outside of region of interest. The effectiveness of DSSD is investigated with phantom and human using an 8-channel parallel transmit 7 Tesla Siemens system. Similar suppression performance was obtained in phantom and human brain using DSSD with a circular and an elliptical shape, respectively. The results show that OVS can be achieved by using a high degree shim insert to generate a steep B0 gradient at periphery of target region.