Flag curvature in Finlser geometry is a generalization of sectional curvature in Riemannian geometry, which enable us to define and study positively curved or negatively curved spaces in Finsler geometry. In this talk, we introduce a weaker version of positive curvature property which only appears in Finsler geometry, i.e. the flag-wise positively curved condition, or (FP) condition for simplicity. We show there exist abundant examples of compact coset spaces which admits non-negatively curved and flag-wise positively curved homogeneous Finsler metrics, but no positively curved homogeneous Finsler metrics. For example, S^2\times S^3 and S^6\times S^7 admits such metrics which seem "very close" to the positively curved ones.