Flow in a circular pipe rotating about its axis, at low Reynolds number, is investigated. The simulation is performed by a finite difference scheme, second-order accurate in space and in time. A non-uniform grid in the radial direction yields accurate solutions with a reasonable number of grid points. The numerical method has been tested for the non-rotating pipe in the limit ν→0 to prove the energy conservation properties. In the viscous case a grid refinement check has been performed and some conclusions about drag reduction have been reached. The mean and turbulent quantities have been compared with the numerical and experimental non-rotating pipe data of Eggels et al. (1994a, b). When the pipe rotates, a degree of drag reduction is achieved in the numerical simulations just as in the experiments. Through the visualization of the vorticity field the drag reduction has been related to the modification of the vortical structures near the wall. A comparison between the vorticity in the non-rotating and in the high rotation case has shown a spiral motion leading to the transport of streamwise vorticity far from the wall.