© 2017 American Physical Society. We report the first measurement of the T-odd moments in the decay D0→KS0π+π-π0 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 aCPT-odd=[-0.28±1.38(stat.)-0.76+0.23(syst.)]×10-3, which is consistent with no CP violation. In addition, we perform aCPT-odd measurements in different regions of the D0→KS0π+π-π0 phase space; these are also consistent with no CP violation.