  In this paper we study flag curvature of invariant $(\alpha,\beta)$-metrics
of the form $\frac{(\alpha+\beta)^2}{\alpha}$ on homogeneous spaces and Lie
groups. We give a formula for flag curvature of invariant metrics of the form
$F=\frac{(\alpha+\beta)^2}{\alpha}$ such that $\alpha$ is induced by an
invariant Riemannian metric $g$ on the homogeneous space and the Chern
connection of $F$ coincides to the Levi-Civita connection of $g$. Then some
conclusions in the cases of naturally reductive homogeneous spaces and Lie
groups are given.
