A measurement of the parity-violating decay asymmetry parameter, α b , and the helicity amplitudes for the decay Λ 0 b → J=ψðμ þ μ − ÞΛ 0 ðpπ − Þ is reported. The analysis is based on 1400 Λ 0 b andΛ 0 b baryons selected in 4.6 fb −1 of proton-proton collision data with a center-of-mass energy of 7 TeV recorded by the ATLAS experiment at the LHC. By combining the Λ 0 b andΛ 0 b samples under the assumption of CP conservation, the value of α b is measured to be 0.30 AE 0.16ðstatÞ AE 0.06ðsystÞ. This measurement provides a test of theoretical models based on perturbative QCD or heavy-quark effective theory.