The CP-violating weak phase phi(s) of the B-s(0) meson and the decay width difference Delta Gamma(s) of the B-s(0) light and heavy mass eigenstates are measured with the CMS detector at the LHC using a data sample of B-s(0)-> J/psi phi(1020) -> mu(+)mu-K+K- decays. The analysed data set corresponds to an integrated luminosity of 19.7 fb(-1) collected in pp collisions at a centre-of-mass energy of 8 TeV. A total of 49200 reconstructed B-s(0) decays are used to extract the values of phi(s) and Delta Gamma(s) by performing a time dependent and flavour-tagged angular analysis of the mu(+)mu-K+K- final state. The weak phase is measured to be phi(s) =-0.075 +/- 0.097 (stat) +/- 0.031 (syst) rad, and the decay width difference is Delta Gamma(s) = 0.095 +/- 0.013 (stat) +/- 0.007 (syst) ps(-1). (C) 2016 CERN for the benefit of the CMS Collaboration. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP(3).