  An inflationary model in the framework of noncommutative space-time may
generate a nontrivial running of the scalar spectral index, but usually induces
a large tensor-to-scalar ratio simultaneously. With the latest observational
data from the Planck mission, we reexamine the inflationary scenarios in a
noncommutative space-time. We find that either the running of the spectral
index is tiny compared with the recent observational result, or the
tensor-to-scalar ratio is too large to allow a sufficient number of $e$-folds.
As examples, we show that the chaotic and power-law inflation models with the
noncommutative effects are not favored by the current Planck data.
