The 2MFGC catalog we have used contains 18020 galaxies selected from the extended objects in the 2MASS infrared sky survey as having apparent ratios of the axes b/a < 0.3. Most of them are spiral galaxies of late morphological types whose discs are seen almost edge-on. The individual distances to the 2724 2MFGC galaxies with known rotation velocities and radial velocities are determined using a multi-parametric infrared Tully-Fisher relation. A list of the distances and peculiar velocities of these galaxies is presented. The bulk motion of the 2MFGC galaxies relative to the cosmic microwave background is characterized with the velocity V = 199±37 km/s in the direction l = 304°±11°, b = -8°±8°. Our list is currently the most representative and uniform sample for analyzing non-Hubble motion of galaxies on a scale of ~100 Mpc.