A measurement of B0s→J/ψϕ decay parameters, including the CP -violating weak phase ϕ s and the decay width difference ΔΓ s is reported, using 4.9 fb−1 of integrated luminosity collected in 2011 by the ATLAS detector from LHC pp collisions at a centre-of-mass energy s√=7 TeV. The mean decay width Γ s and the transversity amplitudes |A 0(0)|2 and |A ∥(0)|2 are also measured. The values reported for these parameters are: ϕs=0.22±0.41 (stat.)±0.10 (syst.) rad; ΔΓs=0.053±0.021 (stat.)±0.010 (syst.) ps−1; Γs=0.677±0.007 (stat.)±0.004 (syst.) ps−1; |A0(0)|2=0.528±0.006 (stat.)±0.009 (syst.); |A∥(0)|2=0.220±0.008 (stat.)±0.007 (syst.) where the values quoted for ϕ s and ΔΓ s correspond to the solution compatible with the external measurements to which the strong phase δ ⊥ is constrained and where ΔΓs is constrained to be positive. The fraction of S-wave KK or f 0 contamination through the decays B0s→J/ψK+K−(f0) is measured as well and is found to be consistent with zero. Results for ϕ s and ΔΓ s are also presented as 68%, 90% and 95% likelihood contours, which show agreement with Standard Model expectations.