Charged-hadron transverse-momentum and pseudorapidity distributions in proton-proton collisions at square root of s = 7 TeV are measured with the inner tracking system of the CMS detector at the LHC. The charged-hadron yield is obtained by counting the number of reconstructed hits, hit pairs, and fully reconstructed charged-particle tracks. The combination of the three methods gives a charged-particle multiplicity per unit of pseudorapidity dN(ch)/dη|(|η|<0.5) = 5.78 ± 0.01(stat) ± 0.23(syst) for non-single-diffractive events, higher than predicted by commonly used models. The relative increase in charged-particle multiplicity from square root of s = 0.9 to 7 TeV is [66.1 ± 1.0(stat) ± 4.2(syst)]%. The mean transverse momentum is measured to be 0.545 ± 0.005(stat) ± 0.015(syst) GeV/c. The results are compared with similar measurements at lower energies.