  In this paper we study the R\'{e}nyi entropy of 2D massless free fermions
perturbed by the $T\bar{T}$ term and the $J\bar{T}$ term at the first order
perturbation. Three cases, the vacuum state of infinite size system with
$T\bar{T}$ perturbation, the excited states of finite size system with
$T\bar{T}$ perturbation, and the vacuum state of infinite size system with
$J\bar{T}$ perturbation, are analyzed. We use the bosonization approach to
calculate the perturbative expansions of R\'{e}nyi entropy. In the bosonization
language the twist operator is known explicitly, with which the computation of
correlators in the perturbative expansion can be simply performed. Moreover, we
show that the $T\bar{T}$ and $J\bar{T}$ terms have a simple form and are
similar with each other. For the first and third cases, we reproduce the known
results for R\'{e}nyi entropy using the bosonization method. While for the
second case, we obtain new results for the excited states.
