  We analyze the thermodynamics of a black hole in a region that contains a
global monopole in the framework of a particular class of a f(R) gravity.
Specifically, we study the case in which df(R)/dR = F(R) is a power law
function of the radial coordinate of the monopole spacetime, i.e., F(r) = 1 +
\psi_n r^n, where \psi_n is the fine-tuned parameter corresponding to the f(R)
gravity. We obtain explicit expressions for the local thermodynamic quantities
of the black hole as a function of the event horizon, the parameter describing
the monopole and the measurable corrections due to the f(R) theory
modifications of the General Relativity. We also discussed the implications of
the particular case of n=2, where the parameter \psi_2 can be related to a
positive cosmological constant, that in monopole presence is characterized by a
non-trivial topology observed as a deficit solid angle.
