  Three-year data of WMAP implies not only a negative running of the spectral
index with large absolute value, but also a large positive running of running
of the spectral index with order of the magnitude $10^{-2}$. We calculate the
running of running in usual inflation model and noncommutative inflation model.
A large tensor-scalar ratio $r\geq 1.23$ is needed in order to fit the WMAP
data in the noncommutative inflation model, which roughly saturates the
observational upper bound on it.
