We consider the estimation of important parameters of a linear combination of order statistics (L-statistic) in a finite population, emphasizing the influence of auxiliary information on the estimation accuracy. Assuming that values of an auxiliary variable are available for all population units, we construct calibrated estimators for the variance of L-statistics and for the parameters, which define one-term Edgeworth expansions of distributions of L-statistics. The gain of the new estimators is demonstrated by the simulation study.