The pseudorapidity distributions of charged hadrons in proton-lead collisions at nucleon-nucleon center-of-mass energies $ \sqrt{s_{\mathrm{NN}}}=5.02 $ and 8.16 TeV are presented. The measurements are based on data samples collected by the CMS experiment at the LHC. The number of primary charged hadrons produced in non-single-diffractive proton-lead collisions is determined in the pseudorapidity range |η${lab}$| < 2.4. The charged-hadron multiplicity distributions are compared to the predictions from theoretical calculations and Monte Carlo event generators. In the center-of-mass pseudorapidity range |η${cm}$| < 0.5, the average charged-hadron multiplicity densities 〈dN${ch}$/dη${cm}$〉${|η}{cm|}$ < 0.5 are 17.31 ± 0.01 (stat) ± 0.59 (syst) and 20.10 ± 0.01 (stat) ± 0.85(syst) at $ \sqrt{s_{\mathrm{NN}}}=5.02 $ and 8.16 TeV, respectively. The particle densities per participant nucleon are compared to similar measurements in proton-proton, proton-nucleus, and nucleus-nucleus collisions.