The molecular dynamics of sodium dodecyl sulfate (SDS) micelle has been investigated using high-resolution incoherent quasielastic neutron scattering technique. Data analysis clearly shows presence of two distinct motions: whole micellar motion or global diffusion and faster internal motion of the SDS monomer. The global diffusion associated with the whole micelle is found to be Fickian in nature, and the corresponding diffusion coefficients are found to be consistent with those obtained from dynamic light scattering measurements. The internal motion is described with a model consistent with the structure of the micelle and which accounts for the flexibility of the chains. The SDS monomer consists of a head group, which lies on the surface of the globular micelle, and a tail that hangs from the head toward the center of the globule. Considering various factors like conformational changes of the SDS chains, bending, stretching of the chemical bonds, etc., the dynamics of the SDS molecules is successfully described by a model in which the hydrogen atoms undergo localized translational motion confined within spherical volumes. This volume increases linearly along the SDS chain such that the hydrogen atoms closer to the head group move within smaller spheres with lower diffusion constant than the hydrogen atoms away from the head group. This model is found to be consistent with the data over the whole temperature and concentration range. Diffusivity and the volume of the spheres are also found to increase with temperature. The effect of lowering the SDS concentration is found to be similar to that of increasing the temperature.