The growth rate of matter perturbation and the expansion rate of the Universe can be used to distinguish modified gravity and dark energy models in explaining the cosmic acceleration . The growth rate is parametrized by the growth index \gamma . We discuss the dependence of \gamma on the matter energy density \Omega and its current value \Omega _ { 0 } for a more accurate approximation of the growth factor . The observational data , including the data of the growth rate , are used to fit different models . The data strongly disfavor the Dvali-Gabadadze-Porrati model . For the dark energy model with a constant equation of state , we find that \Omega _ { 0 } = 0.27 \pm 0.02 and w = -0.97 \pm 0.09 . For the \Lambda CDM model , we find that \gamma = 0.64 ^ { +0.17 } _ { -0.15 } . For the Dvali-Gabadadze-Porrati model , we find that \gamma = 0.55 ^ { +0.14 } _ { -0.13 } .