A measurement of the parity-violating decay asymmetry parameter, αb, and the helicity amplitudes for the decay Λ0b→J/ψ(μ+μ-)Λ0(pπ-) is reported. The analysis is based on 1400 Λ0b and Λ0¯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 Λb0 and Λ0¯b samples under the assumption of CP conservation, the value of αb is measured to be 0.30±0.16(stat)±0.06(syst). This measurement provides a test of theoretical models based on perturbative QCD or heavy-quark effective theory.