Charged-particle production was studied in proton-proton collisions collected at the LHC with the ALICE detector at centre-of-mass energies 0.9 TeV and 2.36 TeV in the pseudorapidity range |{eta}| < 1.4. In the central region (|{eta}| < 0.5), at 0.9 TeV, we measure charged-particle pseudorapidity density d N{sub ch}/d{eta} = 3.02 {+-} 0.01(stat.){sub -0.05}{sup +0.08}(syst.) for inelastic interactions, and d N{sub ch}/d{eta} = 3.58 {+-} 0.01(stat.){sub -0.12}{sup +0.12}(syst.) for non-single-diffractive interactions. At 2.36 TeV, we find d N{sub ch}/d{eta} = 3.77 {+-} 0.01(stat.){sub -0.12}{sup +0.25}(syst.) for inelastic, and d N{sub ch}/d{eta} = 4.43 {+-} 0.01(stat.){sub -0.12}{sup +0.37}(syst.) for non-single-diffractive collisions. The relative increase in charged-particle multiplicity from the lower to higher energy is 24.7% {+-} 0.5%(stat.){sub -2.8}{sup +5.7}%(syst.) for inelastic and 23.7% {+-} 0.5%(stat.){sub -1.1}{sup +4.6}%(syst.) for non-single-diffractive interactions. This increase is consistent with that reported by the CMS collaboration for non-single-diffractive events and larger than that found by a number of commonly used models. The multiplicity distribution was measured in different pseudorapidity intervals and studied in terms of KNO variables at both energies. The results are compared to proton-antiproton data and to model predictions.