© 2016 CERN. © 2016 CERN, for the ALICE Collaboration. Published by the American Physical Society under the terms of the »http://creativecommons.org/licenses/by/3.0/» Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.The pseudorapidity density of charged particles, dNch/dη, at midrapidity in Pb-Pb collisions has been measured at a center-of-mass energy per nucleon pair of sNN=5.02 TeV. For the 5% most central collisions, we measure a value of 1943±54. The rise in dNch/dη as a function of sNN is steeper than that observed in proton-proton collisions and follows the trend established by measurements at lower energy. The increase of dNch/dη as a function of the average number of participant nucleons, Npart, calculated in a Glauber model, is compared with the previous measurement at sNN=2.76 TeV. A constant factor of about 1.2 describes the increase in dNch/dη from sNN=2.76 to 5.02 TeV