We study the estimation of high-dimensional covariance matrices under ellip- tical factor models with 2 + εth moment. For such heavy-tailed data, robust estimators like the Huber-type estimator in Fan et al. (2018) can not achieve sub-Gaussian optimal convergence rates. We develop an idiosyncratic-projected self-normalization (IPSN) method to remove the effect of heavy-tailed scalar pa- rameter, and propose a robust pilot estimator for the scatter matrix. We show that our estimator achieve the optimal sub-Gaussian rate. We further develop a consistent generic POET estimator of the covariance matrix and show that it achieves a faster convergence rate than the generic POET estimator in Fan et al. (2018).