The 2MFGC catalog we have used contains 18020 galaxies selected from among 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 later morphological types whose disks are seen almost edge-on. The individual distances to the 2724 2MFGC galaxies with known rotation velocities and radial velocities are determined using a multiparameter infrared Tully-Fisher relation. A list of the distances and peculiar velocities of these galaxies is presented. The collective motion of the 2MFGC galaxies relative to the cosmic microwave background is characterized by a velocity V=199+/-37km/s in the direction l=304+/-11, b=-8+/-8 . Our list is currently the most representative and uniform sample for analyzing non-Hubble motions of galaxies on a scale of ~100Mpc.