  In this paper we examine the cosmological consequences of fourth order
Galileon gravity. We carry out detailed investigations of the underlying
dynamics and demonstrate the stability of one de Sitter phase. The stable de
Sitter phase contains a Galileon field $\pi$ which is an increasing function of
time (\dot{\pi}>0). Using the required suppression of the fifth force,
supernovae, BAO and CMB data, we constrain parameters of the model. We find
that the $\pi$ matter coupling parameter $\beta$ is constrained to small
numerical values such that $\beta$<0.02. We also show that the parameters of
the third and fourth order in the action (c_3,c_4) are not independent and with
reasonable assumptions, we obtain constraints on them. We investigate the
growth history of the model and find that the sub-horizon approximation is not
allowed for this model. We demonstrate strong scale dependence of linear
perturbations in the fourth order Galileon gravity.
