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The combined effects of the system rotation (Coriolis force) and curvature (centrifugal force) on the flow in rotating curved circular pipe with small curvature are examined by perturbation method. A second-order perturbation solution is presented. The secondary flow structure and the primary axial velocity distributions are studied in detail. The loops of the secondary flow are more complex than those in a curved pipe without rotation or a rotating straight pipe. Its numbers depend on the body force ratio F which represents the ratio of the Coriolis to the centrifugal force. The maximum of the axial velocity is pushed to either outer bend or inner bend, which is also determined by F. The results are confirmed by the results of other authors who studied the same problem by different methods.