The performance of the ATLAS muon trigger system is evaluated with proton-proton collision data collected in 2012 at the Large Hadron Collider at a centre-of-mass energy of 8 TeV. It is primarily evaluated using events containing a pair of muons from the decay of Z bosons. The efficiency of the single-muon trigger is measured for muons with transverse momentum 25 < pT < 100 GeV, with a statistical uncertainty of less than 0.01% and a systematic uncertainty of 0.6%. The pT range for efficiency determination is extended by using muons from decays of J/ψ mesons, W bosons, and top quarks. The muon trigger shows highly uniform and stable performance. The performance is compared to the prediction of a detailed simulation.