  In this paper, by limiting twisted conical K\"ahler-Ricci flows, we prove the
long-time existence and uniqueness of cusp K\"ahler-Ricci flow on compact
K\"ahler manifold $M$ which carries a smooth hypersurface $D$ such that the
twisted canonical bundle $K_M+D$ is ample. Furthermore, we prove that this flow
converge to a unique cusp K\"ahler-Einstein metric.
