An (α, β)-metric is defined by a Riemannian metric α and 1-form β. In this paper, we study a class of (α, β)-metrics F = αφ(β/α) with φ(s) satisfying a known ODE. For any metric F in such a class, we show that in dimension n ≥ 3, F is of scalar flag curvature if and only if F is locally projectively flat, if β is closed. While for a subclass with F being a general square metric type, we prove that in dimension n ≥ 3, F is of scalar flag curvature if and only if F is locally projectively flat.