We consider the acceleration of energetic particles by a velocity shear in the relativistic background flow containing scattering centers. Three possible acceleration sites for astrophysical jets are identified: (1) gradual velocity shear parallel to the jet axis, such as a velocity profile decreasing linearly outward with radial coordinate, (2) gradual velocity shear perpendicular to the jet axis, such as intrinsic jet rotation, and (3) non-gradual/discontinuous, longitudinal velocity shear at the jet-side boundary. We determine the characteristic acceleration timescales, specify the conditions for efficient acceleration and discuss observational features with respect to each process. In particular, it is shown that in the case of (2) the higher energy emission is expected to be concentrated closer to the jet axis, while in the case of (1) and (3) the higher energy particles are likely to be located near the edges of the jet, thus possibly leading to some form of limb-brightening.

18 pages, ApJ in press; final version (small typos corrected to match published version), Journal-ref. added