A measurement of B0 s → J/ψφ decay parameters, including the CP-violating weak phase φs and the decay width difference s is reported, using 4.9 fb−1 of integrated luminosity collected in 2011 by the ATLAS detector from LHC pp collisions at a centreof- mass energy √s = 7 TeV. The mean decay width s and the transversity amplitudes |A0(0)|2 and |Ak(0)|2 are also measured. The values reported for these parameters are: φs = 0.22 ± 0.41 (stat.) ± 0.10 (syst.) rad s = 0.053 ± 0.021 (stat.) ± 0.010 (syst.) ps−1 s = 0.677 ± 0.007 (stat.) ± 0.004 (syst.) ps−1 |A0(0)|2 = 0.528 ± 0.006 (stat.) ± 0.009 (syst.) |Ak(0)|2 = 0.220 ± 0.008 (stat.) ± 0.007 (syst.) where the values quoted for φs and s correspond to the solution compatible with the external measurements to which the strong phase δ⊥ is constrained and where s is constrained to be positive. The fraction of S-wave KK or f0 contamination through the decays B0 s → J/ψK+K−(f0) is measured as well and is found to be consistent with zero. Results for φs and s are also presented as 68%, 90% and 95% likelihood contours, which show agreement with Standard Model expectations.