  We study the axion monodromy inflation with a non-perturbatively generated
sinusoidal term. The potential form is a mixture between the natural inflation
and the axion monodromy inflation potentials. The sinusoidal term is
subdominant in the potential, but leaves significant effects on the resultant
fluctuation generated during inflation. A larger tensor-to-scalar ratio can be
obtained in our model. We study two scenarios, single inflation scenario and
the double inflation scenario. In the first scenario, the axion monodromy
inflation with a sufficient number of e-fold generates a larger
tensor-to-scalar ratio about $0.1 - 0.15$ but also a tiny running of spectral
index. In the second scenario of double inflation, axion monodromy inflation is
its first stage and, we assume another inflation follows. In this case, our
model can realize a larger tensor-to-scalar ratio and a large negative running
of spectral index simultaneously.
