  Dark matter (DM) interacting with the SM fields via a $Z'-$boson
('$Z'$-portal') remains one of the most attractive WIMP scenarios, both from
the theoretical and the phenomenological points of view. In order to avoid the
strong constraints from direct detection and dilepton production, it is highly
convenient that the $Z'$ has axial coupling to DM and leptophobic couplings to
the SM particles, respectively. In this paper we first explore the conditions
for an anomaly-free leptophobic $Z'$, which (if flavour-blind) has to coincide
with that from gauged baryon-number in the SM sector. Then there are very few
possibilities where, besides leptophobia, the coupling to DM is axial; namely
four (quite similar) cases if the content of the dark sector is minimal. The
resulting scenario is very predictive, and perfectly viable from the present
constraints from DM detection, EW observables and LHC data (di-lepton, di-jet
and mono-jet production). We analyze all these constraints, obtaining the
allowed areas in the parameter space, which generically prefer $m_{Z'}\lesssim
500$ GeV, apart from resonant regions. The best chances to test these viable
areas come from future LHC measurements.
