Abstract: To accurately solve the curved slip wall using finite difference methods, this work proposes a boundary constraint algorithm assigning ghost nodes based on discrete equivalents equation that eliminates the coordinate transformation-induced errors. Except for the wall-normal velocity, this method further constrains the wall-normal momentum flux at the wall to zero. The fluxes at the boundary nodes are determined by the physical quantities of ghost nodes by solving the constraint equation. The new method constructs ghost nodes by considering the wall as a streamline and takes the influence of neighboring wall tangential nodes into account, a more reasonable strategy than the traditional weak boundary condition. By doing so, the same discrete scheme can be used through the whole domain, avoiding the scheme compatibility issue near the wall so that the near-wall flow fields can be solved more accurately with the non-penetration wall condition strictly satisfied during time advancement. Typical examples demonstrate that the proposed method, which can be easily integrated into MUSCL and WENO schemes, can effectively reduce the numerical errors in the near-wall region.