  In this note, we study the long time existence of the Calabi flow on $X =
\mathbb{C}^n/\mathbb{Z}^n + i\mathbb{Z}^n$. Assuming the uniform bound of the
total energy, we establish the non-collapsing property of the Calabi flow by
using Donaldson's estimates and Streets' regularity theorem. Next we show that
the curvature is uniformly bounded along the Calabi flow on $X$ when the
dimension is 2, partially confirming Chen's conjecture. Moreover, we show that
the Calabi flow exponentially converges to the flat K\"ahler metric for
arbitrary dimension if the curvature is uniformly bounded, partially confirming
Donaldson's conjecture.
