New solutions are presented to the equilibrium Vlasov-fluid equations in Z-pinch geometry that include the effect of sheared axial ion flow. These are different to previous Vlasov-fluid equilibria in that the ion distribution function shows an axial temperature anisotropy. Examples of three new classes of equilibria are calculated, these being the anisotropic-parabolic (constant current density) and Bennett (constant relative speed) profiles and a set of profiles resulting from assuming that the ion fluid velocity is given by (b1+rp) for b1=−0.5 and p>1.