We present new static spherically-symmetric solutions of Einstein equations with the quintessence-like matter surrounding a global monopole. These new solutions of the coupling scalar-Einstein equations are more complicated, which depend on the parameter of equation of state −1<wq<−13. A gravitating global monopole produces a gravitational field of de Sitter kind outside the core in addition to a solid angular deficit. In the wq=−13 case, we have proved that the solution cannot exist since the density of quintessence-like tends to zero if wq→−13. As a new feature, these monopoles have the outer horizon depending on both Goldstone field and quintessence-like. Since current observations constrain −1.14<wq<−0.93, new global monopoles have interesting astrophysical applications.