We perform an analysis of the D+→ K0Sπ+π0 Dalitz plot using a data set of 2.92 fb-1 of e+e- collisions at the ψ(3770) mass accumulated by the BESIII experiment, in which 166694 candidate events are selected with a background of 15.1%. The Dalitz plot is found to be well represented by a combination of six quasitwo- body decay channels [K0Sρ+, K0Sρ(1450)+, K∗0π+, K0 (1430)0π+, K (1680)0π+, κ0π+] plus a small nonresonant component. Using the fit fractions from this analysis, partial branching ratios are updated with higher precision than previous measurements.