Existing work of designing curves on mesh surface suffers from issues such as weak robustness, slow convergence, and narrow application ranges. To address these issues, a distance constrained approach is proposed, which converts the complicated manifold constraint into distance constraint, and formulates the problem as a constrained optimization combining with smoothness and interpolation (approximation) constraints. To solve the optimization, the curve is discretized into a poly-line, and the distance constraint is relaxed to point-to-plane distance by approximating the local surface patch with tangent plane. Since the curve points and the corresponding tangent points involved in the distance calculation are interdependence, a “local/global” alternating iteration scheme is adopted and the idea of Gauss-Newton method is used to control the convergence behavior. In the global stage, the iterative step is solved by relaxingthe problem into a convex optimization via distance approximation. In the local stage, a robust and efficient projection method is applied to update tangent planes. Finally, each segment of the poly-line is projected onto the surface by cutting planes. Experiments exhibit that the proposed method outperforms existing work on various aspects, including effectiveness, robustness, controllability, and practicability.