  We propose a new class of inflation model, G-inflation, which has a
Galileon-like nonlinear derivative interaction of the form $G(\phi,
(\nabla\phi)^2)\Box\phi$ in the Lagrangian with the resultant equations of
motion being of second order. It is shown that (almost) scale-invariant
curvature fluctuations can be generated even in the exactly de Sitter
background and that the tensor-to-scalar ratio can take a significantly larger
value than in the standard inflation models, violating the standard consistency
relation. Furthermore, violation of the null energy condition can occur without
any instabilities. As a result, the spectral index of tensor modes can be blue,
which makes it easier to observe quantum gravitational waves from inflation by
the planned gravitational-wave experiments such as LISA and DECIGO as well as
by the upcoming CMB experiments such as Planck and CMBpol.
