  The intermediate, logamediate and exponential inflationary models in the
context of Galileon inflation or G-inflation are studied. By assuming a
coupling of the form $G(\phi,X)\propto\phi^{\nu}\,X^{n}$ in the action, we
obtain different analytical solutions from the background cosmological
perturbations assuming the slow-roll approximation. General conditions required
for these models of G-inflation to be realizable are determined and discussed.
In general, we analyze the condition of inflation and also we use recent
astronomical and cosmological observations for constraining the parameters
appearing in these G-inflationary models.
