Measurements of the pseudorapidity distributions of charged hadrons produced in xenon-xenon collisions at a nucleon-nucleon centre-of-mass energy of sNN=5.44 TeV are presented. The measurements are based on data collected by the CMS experiment at the LHC. The yield of primary charged hadrons produced in xenon-xenon collisions in the pseudorapidity range |η|<3.2 is determined using the silicon pixel detector in the CMS tracking system. For the 5% most central collisions, the charged-hadron pseudorapidity density in the midrapidity region |η|<0.5 is found to be 1187±36 (syst), with a negligible statistical uncertainty. The rapidity distribution of charged hadrons is also presented in the range |y|<3.2 and is found to be independent of rapidity around y=0. Existing Monte-Carlo event generators are unable to simultaneously describe both results. Comparisons of charged-hadron multiplicities between xenon-xenon and lead-lead collisions at similar collision energies show that particle production at midrapidity is strongly dependent on the collision geometry in addition to the system size and collision energy.