Abstract: Effect of the orbital motion of an eccentric inner pipe on annular laminar flow is investigated numerically, with the inner pipe rotating, the flow being fully-developed laminar and the fluid in power-law type. The results shows that the orbital motion of the inner pipe always has significant influence on the distribution of pressure and shear stress on the surface of the inner pipe. The orbital motion usually causes the reduction of flow resistance, which has relations with the compression to the secondary flow by the orbital motion and also the shear-thinning effect of the power-law fluid. The variation of the flow resistance with the intensity of the orbital motion is not monotonic. At each eccentricity, there exists a critical intensity for the orbital motion, at which the flow resistance is the lowest.