  As an extension of Dvali-Gabadadze-Porrati (DGP) model, the Galileon theory
has been proposed to explain the "self-accelerating problem" and "ghost
instability problem". In this Paper, we extend the Galileon theory by
considering a non-minimally coupled Galileon scalar with gravity. The
statefinder analysis, $Om(z)$ diagnostic and constraint the model parameters
have been investigate , we find $\Omega_\text{m0}=0.263_{-0.031}^{+0.031}$,
$n=1.53_{-0.37}^{+0.21}$ (at the $95\%$ confidence level) with
$\chi^2_{\text{min}}=473.376$. Further we show that due to the SNe Ia + BAO
data ,our model behaves like a phantom-like dark energy.
