The self-sweeping laser is the simplest sort of tunable laser without use of optical elements and electrical drivers for frequency tuning. Owing to broad sweeping range (more than 10 nm) and simplicity, self-sweeping fiber lasers are attractive sources for applications demanding tunable radiation such as sensors interrogation, spectral analysis, optical frequency domain reflectometry and so on. Currently the self-sweeping effect in fiber lasers was observed in different spectral regions covering range from 1 to 2.1 μm. In the paper, linearly-polarized Tm-doped fiber laser with sweeping range of more than 20 nm in the region of 1.92 μm has been experimentally demonstrated. The laser is based on singlemode polarization-maintaining Tm-doped fiber and pumped by home-made Er-doped fiber laser with wavelength of 1540 nm. The cavity is formed by highly-reflective fiber loop mirror and right-angle cleaved fiber end. The main feature of the laser is generation of periodic μs-scale pulses where each of them contains practically only single longitudinal mode radiation with linewidth of ~1 MHz. The laser frequency is changed from pulse to pulse by one intermode beating frequency of the laser ~8 MHz. The sweeping rate is increased with pump power up to 10 nm/sec. The average output power exceeds 400 mW. The developed laser source can be used for atmospheric remote sensing as well as for interrogation of the sensors based on fiber Bragg gratings and is applied to measure spectrum of water absorption lines in air.