  We examine the accretion process onto the black hole with a string cloud
background, where the horizon of the black hole has an enlarged radius $r_H=2
M/(1-\alpha)$, due to the string cloud parameter $\alpha\; (0 \leq \alpha <
1)$. The problem of stationary, spherically symmetric accretion of a polytropic
fluid is analysed to obtain an analytic solution for such a perturbation.
Generalised expressions for the accretion rate $\dot{M}$, critical radius
$r_s$, and other flow parameters are found. The accretion rate $\dot{M}$ is an
explicit function of the black hole mass $M$, as well as the gas boundary
conditions and the string cloud parameter $\alpha$. We also find the gas
compression ratios and temperature profiles below the accretion radius and at
the event horizon. It is shown that the mass accretion rate, for both the
relativistic and the non-relativistic fluid by a black hole in the string cloud
model, increases with increase in $\alpha$.
