With the proliferation of renewable energy and electric vehicles (EVs), there have been increasing uncertainties in power systems. Identifying the influencing random variables will reduce the effort in uncertainty modeling and improve the controllability of power systems. In this paper, a density-based global sensitivity analysis (GSA) method is proposed to evaluate the influence of uncertainties on islanded microgrids (IMGs). Firstly, the maximum IMG loadability evaluation model is established to assess the distance from the current operation point to the critical operation point. Secondly, the Borgonovo method, which is a density-based GSA method, is used to evaluate the influence of input variables on IMG loadability. Thirdly, to improve GSA efficiency, a modified Kriging model is used to obtain a surrogate model of IMG loadability, and Borgonovo indices are calculated based on the surrogate model. Finally, the proposed method is tested on a 38-bus IMG system. Simulation results are compared with those considering other methods to validate the effectiveness of the proposed method. Energy storage systems are considered to diminish the influence of critical uncertainties on IMG operation.