Abstract: A measurement of B-s(0) -> J/psi phi decay parameters, including the CP-violating weak phase phi(s) and the decay width difference Delta Gamma(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 root s = 7 TeV. The mean decay width Gamma(s) and the transversity amplitudes vertical bar A(0)(0)vertical bar(2) and vertical bar A(parallel to)(0)vertical bar(2) are also measured. The values reported for these parameters are: phi(s) = 0.22 +/- 0.41 (stat.) +/- 0.10 (syst.) rad Delta Gamma(s) = 0.053 +/- 0.021 (stat.) +/- 0.010 (syst.) ps(-1) Gamma(s) = 0.677 +/- 0.007 (stat.) +/- 0.004 (syst.) ps(-1) vertical bar A(0)(0)vertical bar(2) = 0.528 +/- 0.006 (stat.) +/- 0.009 (syst.) vertical bar A(parallel to)(0)vertical bar(2) = 0.220 +/- 0.008 (stat.) +/- 0.007 (syst.) where the values quoted for phi(s) and Delta Gamma(s) correspond to the solution compatible with the external measurements to which the strong phase delta(perpendicular to) is constrained and where is Delta Gamma(s) constrained to be positive. The fraction of S-wave KK or f(0) contamination through the decays B-s(0) -> J/psi K+K- (f(0)) is measured as well and is found to be consistent with zero. Results for phi(s) and Delta Gamma(s) are also presented as 68%, 90% and 95% likelihood contours, which show agreement with Standard Model expectations.