A measurement of the CP asymmetry in D-0 -> (KSKS0)-K-0 decays is reported, based on a data sample of proton-proton collisions collected by the LHCb experiment from 2015 to 2018, corresponding to an integrated luminosity of 6 fb(-1). The flavor of the D-0 candidate is determined using the charge of the D-*+/- meson, from which the decay is required to originate. The D-0 -> K+K- decay is used as a calibration channel. The time-integrated CP asymmetry for the D-0 -> (KSKS0)-K-0 mode is measured to be A(CP)(D-0 -> (KSKS0)-K-0) = (-3.1 +/- 1.2 +/- 0.4 +/- 0.2), where the first uncertainty is statistical, the second is systematic, and the third is due to the uncertainty on the CP asymmetry of the calibration channel. This is the most precise determination of this quantity to date.