Abstract: A steady incompressible viscous flow in a helical pipe with lowReynolds number (R < 17/ε~(1/ε) ) is investigated by the perturbation method and the usage of helical coordinate system. A second order solution is fully presented. Results show that the torsion of the pipe has turning and deforming effects on the secondary vortices. As Reynolds number increases from, two vortices of the secondary flow turn around a left-right position to an up-down position.