  Let $\mathbb{G}_a$ be the additive group of the field of complex numbers
$\mathbb{C}$. We say that an irreducible algebraic variety $X$ of dimension $n$
admits an additive action if there is a regular action of the group
$\mathbb{G}_a^n = \mathbb{G}_a \times \ldots \times \mathbb{G}_a$ ($n$ times)
on $X$ with an open orbit. In 2017 Baohua Fu and Jun-Muk Hwang introduced a
class of Euler-symmetric varieties. They gave a classification of
Euler-symmetric varieties and proved that any Euler-symmetric variety admits an
additive action. In this paper we show that in the case of projective toric
varieites the converse is also true. More precisely, a projective toric variety
admitting an additive action is an Euler-symmetric variety with respect to any
linearly normal embedding into a projective space. Also we discuss some
properties of Euler-symmetric projective toric varieties.
