We report a study of the decay D-0 -> (KSKS0)-K-0 using 921 fb(-1) of data collected at or near the (sic)(4S) and (sic)(5S) resonances with the Belle detector at the KEKB asymmetric energy e(+)e(-) collider. The measured time-integrated CP asymmetry is A(CP)(D-0 -> (KSKS0)-K-0) = (-0.02 +/- 1.53 +/- 0.02 +/- 0.17)%, and the branching fraction is B(D-0 -> (KSKS0)-K-0) = (1.321 +/- 0.023 +/- 0.036 +/- 0.044) x 10(-4), where the first uncertainty is statistical, the second is systematic, and the third is due to the normalization mode (D-0 -> K-S(0)pi(0)). These results are significantly more precise than previous measurements available for this mode. The A(CP) measurement is consistent with the standard model expectation.