In this Letter, the ALICE Collaboration presents the first measurements of the charged-particle multiplicity density, dN_ch/dη and total charged-particle multiplicity, N_ch ^tot, in Xe–Xe collisions at a centre-of-mass energy per nucleon–nucleon pair of s_NN=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 dN_ch/dη at mid-rapidity and N_ch ^tot for central collisions, normalised to the number of nucleons participating in the collision (N_part) as a function of s_NN follow the trends established in previous heavy-ion measurements. The same quantities are also found to increase as a function of N_part, 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 N_part. 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%.