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 $2��$ C.L., the viable values of $N_{k}$ $e$-folds would satisfy $42\lesssim N_{k}\lesssim 87$ and the rainbow parameter $��$ is nicely constrained to be $��\lesssim6.0$.

10 pages, 3 figures. v2: corrections and improvement, version to appear in PRD