The pseudorapidity distribution of charged hadrons in pp collisions at s=13 TeV is measured using a data sample obtained with the CMS detector, operated at zero magnetic field, at the CERN LHC. The yield of primary charged long-lived hadrons produced in inelastic pp collisions is determined in the central region of the CMS pixel detector (|η|<2) using both hit pairs and reconstructed tracks. For central pseudorapidities (|η|<0.5), the charged-hadron multiplicity density is dNch/dη||η|<0.5=5.49±0.01(stat)±0.17(syst), a value obtained by combining the two methods. The result is compared to predictions from Monte Carlo event generators and to similar measurements made at lower collision energies.