  In this paper, we study the Starobinsky model of inflation in the context of
gravity's rainbow theory. We propose that gravity rainbow functions can be
written in the power-law form of the Hubble parameter. We present a detailed
derivation of the spectral index of curvature perturbation and the
tensor-to-scalar ratio and compare the predictions of our models with Planck
2015 data. We discover that in order to be consistent with Planck data up to
$2\sigma$ C.L., the viable values of $N_{k}$ $e$-folds would satisfy
$42\lesssim N_{k}\lesssim 87$ and the rainbow parameter $\lambda$ is nicely
constrained to be $\lambda \lesssim6.0$.
