The presence of extreme events gives rise to outrageous results regarding population parametersand their estimates using traditional moments. Traditional moments are usually influenced by extremeobservations. In this paper, we propose some new calibration estimators under L-Moments scheme for variance which is one of the most important population parameters. Some suitable calibration constraints under double stratified random sampling are also defined for these estimators. Our proposed estimators based on L-Moments are relatively more robust in presence of extreme values. The empirical efficiency of proposed estimators is also calculated through simulation. Covid-19 pandemic data from January 22, 2020, to August 23, 2020, is considered for simulation study.