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 , the single inflation scenario and the double inflation scenario .
In the first scenario , the axion monodromy inflation with a sufficient number of e-folds generates a larger tensor-to-scalar ratio of about 0.1-0.15 but also a tiny running of the 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 the spectral index simultaneously .