In this paper, under the ellipsoidal channel covariance errors, we investigate robust optimization for artificial noise (AN)-aided wireless information and power transfer with secrecy outage constraint in a two-tier wireless-powered heterogeneous network (HeNet). In this considered network, one femtocell consisting of multiple femtocell users (FUs) is deployed under the coverage of one macrocell consisting of multiple macrocell users (MUs), where FUs can receive information and harvest energy from the femtocell base station (FBS) simultaneously. Meanwhile, multiple eavesdroppers attempt to wiretap the confidential messages intended for FUs. To secure the information and power transfer, AN is injected into the downlink signal of the FBS simultaneously. Moreover, while satisfying the constraints on the signal-to-interference plus-noise ratio requirement at each MU, energy harvesting and secrecy outage probability requirement at each FU the transmit beamforming and AN vectors of the macrocell base station (MBS) and FBS are jointly designed to minimize the total transmit power (MTP). Due to the secrecy outage constraint and channel state information (CSI) errors, this MTP problem is non-convex and contains infinite constraints, which cannot be solved directly. Resorting to the first-order Taylor expansion, Lagrange dual theory and the semi-definite relaxation (SDR) technique, we reformulate the original problem into a solvable form. Then, based on the convex reformulations, we further propose a successive convex approximation (SCA) algorithm for iteratively obtaining the optimal design. Simulation results are finally presented and demonstrate the effectiveness and security of our proposed robust design.