In the previous paper (Li, X. Z., Xi, P., Zhai, X. H.: Phys. Lett. B666, 125-130 (2008)), we show the solutions of Einstein equations with static spherically-symmetric quintessence-like matter surrounding a global monopole. Furthermore, this monopole become a black hole with quintessence-like matter and a deficit solid angle when it is swallowed by an ordinary black hole. We study its quasinorm...