  We derive an exact, axially symmetric solution representing stationary
accretion of the relativistic, collisionless Vlasov gas onto a moving
Schwarzschild black hole. The gas is assumed to be in thermal equilibrium at
infinity, where it obeys the Maxwell-J\"{u}ttner distribution. The Vlasov
equation is solved analytically in terms of suitable action-angle variables. We
provide explicit expressions for the particle current density and accretion
rates. In the limit of infinite asymptotic temperature of the gas, we recover
the qualitative picture known form the relativistic Bondi-Hoyle-Lyttleton
accretion of the perfect gas with the ultra-hard equation of state, in which
the mass accretion is proportional to the Lorentz factor associated with the
black-hole velocity. For a finite asymptotic temperature, the mass accretion
rate is not in general a monotonic function of the velocity of the black hole.
