  In this work, we examine cosmological constraints on models of composite
inflation based on the slow-roll approximation by using the recent Planck
measurement. We compare the spectral index of curvature perturbation (and its
running) and the tensor-to-scalar ratio predicted by such models with Planck
2015 data. We find that the predictions of technicolor inflation are nicely
consistent with the Planck analysis. Moreover, the predictions from the second
model, glueball inflation, are in good agreement with the Planck data at
$2\sigma$C.L. However, the final two models, super glueball inflation and
orientifold inflation, favor only the rather large value of the
tensor-to-scalar ratio of which the predictions are in tension with the Planck
analysis.
