Adaptive kernel density estimator is an efficient estimator when the density to be estimated has long tail or multi-mode. They use varying bandwidths at each observation point by adapting a fixed bandwidth for data. It is well-known that bandwidth selection is too important for performance of kernel estimators. An efficient recent method is the generalized least square cross-validation which improves the least squares cross-validation. In this paper, performances of the adaptive kernel estimators obtained based on the generalized least square crossvalidationareinvestigated. Weperformedasimulationstudytoinform about performances of the modified adaptive kernel estimators. For the simulation, we use also the bandwidth selection methods of normal reference, least squares cross-validation, biased cross-validation, and plug-in methods. Simulation study shows that the adaptive kernel estimators improve the performances of the kernel estimators with fixed bandwidth selected based on generalized least square cross-validation.