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 < w _ { q } < - \frac { 1 } { 3 } .
A gravitating global monopole produces a gravitational field of de Sitter kind outside the core in addition to a solid angular deficit .
In the w _ { q } = - \frac { 1 } { 3 } case , we have proved that the solution can not exist since the density of quintessence-like tends to zero if w _ { q } \rightarrow - \frac { 1 } { 3 } .
As a new feature , these monopoles have the outer horizon depending on both Goldstone field and quintessence-like .
Since current observations constrain -1.14 < w _ { q } < -0.93 , new global monopoles have interesting astrophysical applications .