  In this paper we study the regular self-gravitating 't Hooft-Polyakov
magnetic monopole in a global monopole spacetime. We show that for the large
distance, the structure of the manifold corresponds to the
Reissner-Nordstr\"{o}m spacetime with a solid angle deficit factor. Although we
analyze static and spherically symmetric solutions, it is not possible to solve
analytically the system of coupled differential equations and only numerical
evaluations can provide detailed information about the behavior of this system
at the neighborhood of the defect's core. So, for this reason we solve
numerically the set of differential equations for the metric tensor and for the
matter fields for different values of the Higgs field vacuum expectation value,
$\eta$, and the self-coupling constant, $\lambda$.
