We consider multidimensional cosmological model with a higher-dimensional product manifold M = R×R^d₀×H^d₁/Γ where R^d₀ is d₀-dimensional Ricci-flat external (our) space and H^d₁/Γ is d₁-dimensional compact hyperbolic internal space. M2-brane solution for this model has the stage of accelerating expansion of the external space. We apply this model to explain the late time acceleration of our Universe. Recent observational data (the Hubble parameter at the present time and the redshift when the deceleration parameter changes its sign) fix fully all free parameters of the model. As a result, we find that considered model has too big size of the internal space at the present time and variation of the effective four-dimensional fine structure constant strongly exceeds the observational limits.