The present invention is to provide a fine filter structure including two filter units, wherein the first filter unit comprises an upper frame, a coarse screen laid over top side of the upper frame, and a post having a top end formed with at least one through hole, a bottom end fixedly provided on top side of the coarse screen, and a channel in communication with each through hole and bottom side of the coarse screen; and the second filter unit comprises a lower frame and a fine screen laid over top side of the lower frame and having more mesh openings per unit area than the coarse screen. The top side of the lower frame can be connected with the bottom side of the upper frame so as not only to form a single unit but also to form a re-filtration space between the coarse screen and fine screen.