In this Letter, the ALICE Collaboration presents the first measurements of the charged-particle multiplicity density, dNch/dη, and total charged-particle multiplicity, Nchtot, in Xe–Xe collisions at a centre-of-mass energy per nucleon–nucleon pair of sNN=5.44TeV. The measurements are performed as a function of collision centrality over a wide pseudorapidity range of −3.5<η<5. The values of dNch/dη at mid-rapidity and Nchtot for central collisions, normalised to the number of nucleons participating in the collision (Npart) as a function of sNN follow the trends established in previous heavy-ion measurements. The same quantities are also found to increase as a function of Npart, and up to the 5% most central collisions the trends are the same as the ones observed in Pb–Pb at a similar energy. For more central collisions, the Xe–Xe scaled multiplicities exceed those in Pb–Pb for a similar Npart. The results are compared to phenomenological models and theoretical calculations based on different mechanisms for particle production in nuclear collisions. All considered models describe the data reasonably well within 15%.