We present calculations of the g factors of hole quantum wires for a magnetic field in the vertical (growth) direction. The energy bands are symmetric with respect to wavenumber inversion and the obtained g factors are larger than those for in-plane fields. For high-enough wire deformations, the g-factors are quenched when the Rashba interaction is increased. A Rashba-induced anisotropy similar to the horizontal one is thus predicted. A simple perturbative model explains qualitatively the numerical results.