In this paper, the numerical investigation of a Bondi–Hoyle accretion around a non-rotating black hole in a novel four dimensional Einstein–Gauss–Bonnet gravity is investigated by solving the general relativistic hydrodynamical equations using the high resolution shock capturing scheme. For this purpose, the accreated matter from the wind-accreating X-ray binaries falls towards the black hole from the far upstream side of the domain, supersonically. We study the effects of Gauss–Bonnet coupling constant $$\alpha $$
α
in 4D EGB gravity on the accreated matter and shock cones created in the downstream region in detail. The required time having the shock cone in downstream region is getting smaller for $$\alpha > 0$$
α
>
0
while it is increasing for $$\alpha < 0$$
α
<
0
. It is found that increases in $$\alpha $$
α
leads violent oscillations inside the shock cone and increases the accretion efficiency. The violent oscillations would cause increase in the energy flux, temperature, and spectrum of X-rays. So the quasi-periodic oscillations (QPOs) are naturally produced inside the shock cone when $$-5 \le \alpha \le 0.8$$
-
5
≤
α
≤
0.8
. It is also confirmed that EGB black hole solution converges to the Schwarzschild one in general relativity when $$\alpha \rightarrow 0$$
α
→
0
. Besides, the negative coupling constants also give reasonable physical solutions and increase of $$\alpha $$
α
in negative directions suppresses the possible oscillation observed in the shock cone.