In computational advertising, a challenging problem is how to recommend the bid for advertisers to achieve the best return on investment (ROI) given budget constraint. This paper presents a bid recommendation scenario that discovers the concavity changes in click prediction curves. The recommended bid is derived based on the turning point from significant increase (i.e. concave downward) to slow increase (convex upward). Parametric learning based method is applied by solving the corresponding constraint optimization problem. Empirical studies on real-world advertising scenarios clearly demonstrate the performance gains for business metrics (including revenue increase, click increase and advertiser ROI increase).