The study of curvature properties of homogeneous Finsler spaces with (?,?)-metrics is one of the central problems in Riemann-Finsler geometry. In this paper, the existence of invariant vector fields on a homogeneous Finsler space with square metric is proved. Further, an explicit formula for S-curvature of a homogeneous Finsler space with square metric is established. Finally, using the formula of S-curvature, the mean Berwald curvature of aforesaid (?,?)-metric is calculated.
