The diffusive properties of an imidazolium room-temperature ionic liquid (RTIL), 1,2-dimethyl-3-propylimidazolium bis(trifluoromethylsulfonyl)amide (DMPImTFSA), are studied from the ionic conductivity and the ion diffusion coefficients measured by pulsed field gradient spin echo NMR. The temperature-dependent H-1, F-19, and C-13 NMR spin-lattice relaxation time T-1 values were observed, and the H-1 T-1 for DMPlm showed T-1 minima for various protons. According to the Bloemberger-Purcell-Pound (BPP) equation, the correlation time tau(c) values were directly calculated from H-1 NMR. By using the H-1 tau(c) values, an evaluation of the C-13 T-1 was attempted for the carbons having protons. The tau(c) estimated for molecular motions of DMPIm changes from 1.3 ns at 253 K to 72 ps at 353 K. The Stokes-Einstein-Debye (SED) model suggests that the tau(c) is too short for the overall molecular reorientation near room temperature. Consequently, the possibility of small-angle molecular rotation is proposed and tentative flip angles are calculated by using the translational diffusion coefficient, the bulk viscosity measured in this study, and the tau(c) obtained from H-1 T-1 data in the temperature range between 283 and 353 K. The flip amplitude increases with the temperature. DMPlm has isotropic reorientational motions with temperature-dependent amplitude, in addition to fast intramolecular motions such as methylene segmental motions, methyl rotational motion, and conformational exchange of the imidazolium ring. The existence of fast motions of TFSA is also shown. The translational diffusion of the ions is the slowest dynamic process in the present RTIL. Ab initio molecular orbital calculations are performed to understand the geometries of stable complexes of DMPIm(+) and TFSA(-), and the formation energies from the isolated ions are evaluated. The computed results are important for interpreting the H-1 T-1 behaviors observed for the imidazolium ring protons.