The ATLAS detector has been designed to have good muon momentum resolution up to momenta in the TeV range. The muon momentum resolution of the ATLAS spectrometer has been measured with p-p collision data recorded in 2011. The measurement combines the di-muon mass resolution in J/ψ → μμ and Z → μμ decays with measurements of the alignment accuracy of the detector based on straight muon tracks, which are acquired with special runs without magnetic field in the ATLAS detector.