Let L be a simply-connected simple connected algebraic group over number field F, and H semisimple absolutely maximal F-subgroup of L. $$\Delta (H)$$ the image diagonally embedded in $$L^n$$ . Under cohomological condition, we prove an asymptotic formula for rational points bounded height on projective equivariant compactifications (H)\backslash L^n$$ with respect to balanced line bundle.