  Within the framework of the recent Eddington-inspired Born-Infeld (EiBI)
theory we study gravitational field around an $SO(3)$ global monopole. The
solution also suffers from the deficit solid angle as in the Barriola-Vilenkin
metric but shows a distinct feature that cannot be transformed away unless in
the vanishing EiBI coupling constant, $\kappa$. When seen as a black hole
eating up a global monopole, the corresponding Schwarzschild horizon is shrunk
by $\kappa$. The deficit solid angle makes the space is globally not Euclidean,
and to first order in $\kappa$ (weak-field limit) the deflection angle of light
is smaller than its Barriola-Vilenkin counterpart.
