  The aim of this paper is to give a sufficient and necessary condition of the
generalized polynomial Li\'enard system with a global center (including linear
typer and nilpotent type). Recently, Llibre and Valls [J. Differential
Equations, 330 (2022), 66-80] gave a sufficient and necessary condition of the
generalized polynomial Li\'enard system with a linear type global center. It is
easy to see that our sufficient and necessary condition is more easy by
comparison. In particular, we provide the explicit expressions of all the
generalized polynomial Li\'enard differential systems of degree 5 having a
global center at the origin and the explicit expression of a generalized
polynomial Li\'enard differential system of indefinite degree having a global
center at the origin.
