The determination of track reconstruction efficiencies at LHCb using J/psi -> mu(+)mu(-) decays is presented. Efficiencies above 95% are found for the data taking periods in 2010, 2011, and 2012. The ratio of the track reconstruction efficiency of muons in data and simulation is compatible with unity and measured with an uncertainty of 0.8% for data taking in 2010, and at a precision of 0.4% for data taking in 2011 and 2012. For hadrons an additional 1.4% uncertainty due to material interactions is assumed. This result is crucial for accurate cross section and branching fraction measurements in LHCb.