Estimation of finite population totals in the presence of auxiliary information is considered. A class of estimators based on local polynomial regression is proposed. Like generalized regression estimators, these estimators are weighted linear combination of study variables, in which the eights are calibrated to known control totals, but the assumptions on the super population model are considerably weaker. The estimators are shown to be asymptotically model-unbiased and consistent under mild assumptions. Simulation experiments indicate that the local polynomial regression estimator is more efficient than regression estimators when the model regression function is incorrectly specified, while being approximately as efficient when the parametric specification is correct.