  In this work, we study the H\"older regularity of the K\"ahler- Ricci flow
on compact K\"ahler manifolds with semi-ample canonical line bundle. By
adapting the method in the work of Hein-Tosatti on collapsing Calabi-Yau
metrics, we obtain a uniform spatial H\"older estimate of the K\"ahler-Ricci
flow for all time.
