  We study the inflation scenario with the non-minimally derivative coupling
$XR^{(3)}$, where $X=\nabla_\mu\phi \nabla^\mu\phi$, $\phi$ is the inflaton and
$R^{(3)}$ is the 3-dimensional intrinsic Ricci scalar on the spacelike
hypersurface, and analytically calculate the corrections of $XR^{(3)}$ on the
power spectra of primordial perturbations. It is found that for the $\phi^2$
inflation model, the corresponding predictions can be driven to the best-fit
region of the $n_s$-$r$ diagram.
