Tm3+-doped fluorotellurite fibers (TDFTFs) are fabricated by using a rod-in-tube method. A 2.1 m long TDFTF is used as the gain medium, in which both ends of the TDFTF are connected to a short piece of a silica fiber by direct fusion splicing. By inserting the above TDFTF and a tunable optical bandpass filter into a ring cavity and employing a 1400/1570 nm dual-wavelength pumping technique, tunable lasing from 1460 to 1526 nm is obtained, which almost covers the whole S-band. To the best of our knowledge, this is the first report of tunable Tm3+-doped fiber laser with a tunable range almost covering the whole S-band. Furthermore, by removing the tunable optical bandpass filter from the ring cavity, free-running multi-wavelength lasers at 1500 and 1901 nm are achieved. Our results show that TDFTFs are promising gain media for constructing S-band fiber lasers.