  Peculiar velocity encodes rich information about the formation, dynamics,
evolution, and merging history of binary black holes. In this work, we employ a
hierarchical Bayesian model to infer the peculiar velocity distribution of
binary black holes. We use the data from GWTC-3 and assume a Maxwell-Boltzmann
distribution for the peculiar velocities, but do not consider the dependence of
peculiar velocity on the masses of black hole binaries. The constraint on the
peculiar velocity distribution parameter, $v_0$, is weak and uninformative.
However, the determination of peculiar velocity distribution can be
significantly improved with next-generation ground-based gravitational wave
detectors. For the Einstein Telescope, the relative uncertainty of $v_0$ will
reduce to $\sim$ 10\% using $10^3$ golden binary black hole events. Our
statistical approach thus provides a robust and prospective inference for
determining the peculiar velocity distribution.
