To reproduce sound field accurately, local sound field synthesis(Local SFS) with virtual loudspeakers that are placed densely around a local listening area have been proposed. In local SFS, it is necessary to limit the size of the listening area. Thus, a listener's head can move out of a listening area due to the natural movement of the listener. In this paper, we propose the concept of a dynamic sound field synthesis system which can moves the sound field synthesis area so as to track the listener's head to allow the listener's movement. For the purpose of facilitating the construction of the massive loudspeaker system in an ordinary room, we utilize a playback system based on a high-speed 1-bit signal that can directly drive a loudspeaker. The proposed system can move the listening area by switching the corresponding local SFS signals obtained from the database including the source signals convolved with the driving functions to reproduce the multiple local area. In simulation experiments, reproduction errors of dynamic local and ordinary SFSs for a plane wave are compared to evaluate the accuracy of sound field by dynamic local SFS.