  A probability of distinguishing between $\Lambda$CDM model and modified
gravity is studied by using the future observations for the growth rate of
cosmic structure (Euclid redshift survey). Adopting extended DGP model, Kinetic
Gravity Braiding model, and Galileon model as modified gravity, we compare
predicted cosmic growth rate by models to the mock observational data. The
growth rate $f\sigma_8$ in the original DGP model is suppressed compared with
the $\Lambda$CDM case, for the same value of the current density parameter of
matter $\Omega_{m,0}$, because of the suppression of effective gravitational
constant. In case of the kinetic gravity braiding model and the Galileon model,
the growth rate $f\sigma_8$ is enhanced compared with the $\Lambda$CDM case,
for the same value of $\Omega_{m,0}$, because of the enhancement of effective
gravitational constant. For future observational data of the cosmic growth rate
(Euclid), compatible value of $\Omega_{m,0}$ are different by models,
furthermore $\Omega_{m,0}$ can be stringently constrained. Thus, we find the
$\Lambda$CDM model is distinguishable from modified gravity by combining the
growth rate data of the Euclid with other observations.
