  We examine the accretion of matter onto a black hole in
scalar--tensor--vector gravity (STVG) also known as modified gravity (MOG). The
gravitational constant is $G=G_{N} (1 + \alpha)$ where $\alpha$ is a parameter
taken to be constant for static black holes in the theory. The MOG black hole
is spherically symmetric and characterised by two event horizons. The matter
falling into the black hole obeys the polytrope equation of state and passes
through two critical points before entering the outer horizon. We obtain
analytical expressions for the mass accretion rate as well as for the outer
critical point, critical velocity and critical sound speed. Our results
complement existing strong field tests like lensing and orbital motion and
could be used in conjunction to determine observational constraints on MOG.
