  In this paper we study the Type IIb mean curvature flow. We first prove that
if the convex entire graph $(y,u(|y|))$ over $\mathbb{R}^n$, $n\geq 2$,
satisfying there exist positive constants $\epsilon$, $c$ and $N$ such that $
u'(r)\geq c r^{\epsilon} $ for $r\geq N$, the longtime solution to mean
curvature flow with initial data $(y,u(|y|))$ must be Type IIb. We also study
the asymptotic behavior of Type IIb mean curvature flow and show that the limit
of suitable rescaling sequence for mean-convex Type IIb mean curvature flow
satisfying $\delta$-Andrews' noncollapsing condition is translating soliton.
