Fair classification which enforces a fairness constraint on the original learning problem is an emerging topic in machine learning. Due to its non-convexity and non-discontinuity, the original (true) fairness constraint is normally relaxed to a convex and smooth surrogate which could lead to slightly deviated solutions and could violate the original fairness constraint. To re-calibrate with the original constraint, existing methods usually hand-tunes a hyper-parameter of the convex surrogate. Such a method is obviously time consuming, besides it cannot guarantee to find the fairer classifier (i.e., original fairness constraint is less than a smaller threshold). To address this challenging problem, we propose a novel true fairness score path algorithm which guarantees to find fairer classifiers efficiently. Specifically, we first give a new formulation of fair classification which treats the surrogate fairness constraint as an additional regularization term, with a fairness hyper-parameter controlling the degree of surrogate fairness. Then, we propose a solution path algorithm which tracks the solutions of fair classification regarding to the fairness hyper-parameter. Based on the solution path, we further propose a true fairness score path algorithm which derives the curve of fairness score with respect to the fairness hyper-parameter and allows us to find the fairer classifiers. Finally, extensive experimental results not only verify the effectiveness of our algorithm, but also show that we can find the fairer classifiers efficiently.