Within the framework of Brans-Dicke gravity, we investigate inflation with the quartic potential, $\lambda\varphi^4/4$, in the presence of generalized Brans-Dicke parameter $\omega_{\rm GBD}(\varphi)$. We obtain the inflationary observables containing the scalar spectral index, the tensor-to-scalar ratio, the running of the scalar spectral index and the equilateral non-Gaussianity parameter in terms of general form of the potential $U(\varphi)$ and $\omega_{\rm GBD}(\varphi)$. For the quartic potential, our results show that the predictions of the model are in well agreement with the Planck 2015 data for the generalized Brans-Dicke parameters $\omega_{\rm GBD}(\varphi)=\omega_0\varphi^{n}$ and $\omega_0e^{b\varphi}$. This is in contrast with both the Einstein and standard Brans-Dicke gravity, in which the result of quartic potential is disfavored by the Planck data.
