  In this work, we study the $f(R)$ models of inflation in the context of
gravity's rainbow theory. We choose three types of $f(R)$ models:
$f(R)=R+\alpha (R/M)^{n},\,f(R)=R+\alpha R^{2}+\beta R^{2}\log(R/M^{2})$ and
the Einstein-Hu-Sawicki model with $n,\,\alpha,\,\beta$ being arbitrary real
constants. Here $R$ and $M$ are the Ricci scalar and mass scale, respectively.
For all models, the rainbow function is 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 results with the latest Planck 2018 data. With the sizeable
number of e-foldings and proper choices of parameters, we discover that the
predictions of all $f(R)$ models present in this work are in excellent
agreement with the Planck analysis.
