  Let $(X,\Delta)$ be a dlt log Calabi-Yau pair admitting a polarized
endomorphism. We show that $(X,\Delta)$ is a finite quotient of a toric log
Calabi-Yau fibration over an abelian variety. We provide an example which shows
that the previous statement does not hold if we drop the dlt condition of
$(X,\Delta)$ even if $X$ is a smooth variety. Given a klt type variety $X$ and
a log Calabi-Yau pair $(X,\Delta)$ admitting a polarized endomorphism, we show
that a suitable birational modification of $(X,\Delta)$ is a finite quotient of
a toric log Calabi-Yau fibration over an abelian variety.
