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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 $\\chi^2_{\\text{min}}=473.376$. 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