This paper presents a study of the performance of the muon reconstruction in the analysis of proton-proton collisions at root s = 7TeV at the LHC, recorded by the ATLAS detector in 2010. This performance is described in terms of reconstruction and isolation efficiencies and momentum resolutions for different classes of reconstructed muons. The results are obtained from an analysis of J/psi meson and Z boson decays to dimuons, reconstructed from a data sample corresponding to an integrated luminosity of 40 pb(-1). The measured performance is compared to Monte Carlo predictions and deviations from the predicted performance are discussed.