Gauging the global (B-L) (Baryon number minus Lepton number) symmetry in the standard model (SM) is well motivated since anomaly cancellations require the introduction of three right-handed neutrinos which play an essential role in naturally generating tiny SM neutrino masses through the seesaw mechanism. In the context of the (B-L) extended SM, we propose a pseudo-Goldstone boson dark matter (DM) scenario in which the imaginary component of a complex (B-L) Higgs field serves as the DM in the universe. The DM relic density is determined by the SM Higgs boson mediated process, but its elastic scattering with nucleons through the exchange of Higgs bosons is highly suppressed due to its pseudo-Goldstone boson nature. The model is therefore free from the constraints arising from direct DM detection experiments. We identify regions of the model parameter space for reproducing the observed DM density compatible with the constraints from the Large Hadron Collider and the indirect DM searches by Fermi Large Area Telescope and Major Atmospheric Gamma Imaging Cherenkov.