We report the first measurement of the T-odd moments in the decay D-0 -> K-S(0) pi + pi(-)pi(0) from a data sample corresponding to an integrated luminosity of 966 fb(-1) collected by the Belle experiment at the KEKB asymmetric-energy e(+)e(-) collider. From these moments we determine the CP-violation-sensitive asymmetry a(CP)(T-odd) = [-0.28 +/- 1.38 (stat.)(-0.76)(+0.23) (syst.)] x 10(-3) , which is consistent with no CP violation. In addition, we perform a(CP)(T-odd) measurements in different regions of the D-0 -> K-S(0) pi + pi(-)pi(0) phase space; these are also consistent with no CP violation.