  In this paper we prove that there is no $\kappa$-solution of Ricci flow on
3-dimensional noncompact manifold with strictly positive sectional curvature
and blow up at some finite time $T$ satisfying $\int^T_0 \sqrt{T-t} R(p_0,t)dt<
\infty$ for some point $p_0$. This partially confirms a conjecture of Perelman.
