Charged-hadron transverse-momentum and pseudorapidity distributions in proton-proton collisions at root 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)/d eta vertical bar(vertical bar eta vertical bar<0.5) = 5.78 +/- 0.01(stat) +/- 0.23(stat) for non-single-diffractive events, higher than predicted by commonly used models. The relative increase in charged-particle multiplicity from root 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.