  The holonomy of the Bismut connection on Vaisman manifolds is studied. We
prove that if $M^{2n}$ is endowed with a Vaisman structure, then the holonomy
group of the Bismut connection is contained in U$(n-1)$. We compute explicitly
this group for particular types of manifolds, namely, solvmanifolds and some
classical Hopf manifolds.
