In this paper, we consider an intelligent reflecting surface (IRS)-aided full-duplex (FD) wireless-powered communication network (WPCN), where a hybrid access point (HAP) operating in FD mode sends information signals to a device in the downlink (DL) and meanwhile receives energy signals from a power station (PS) in the uplink (UL) with the help of an IRS. Our objective is to maximize the achievable data rate from the HAP to the device by jointly optimizing the transmit covariance matrix at the PS, the transmit beamforming vector at the HAP, and the phase shift vector at the IRS. The optimal transmit beamformer at the HAP is derived in closed from, and the joint optimization of the transmit covariance matrix at the PS and the phase shift vector at the IRS results in an intractable non-convex problem. To tackle this challenge, we propose an efficient penalty-based algorithm consisting of two layers. In the inner layer, we iteratively increase the device's signal-to-interference-plus-noise ratio (SINR) by applying the Dinkelbach's transform. While in the outer layer, we gradually decrease the penalty parameter. Numerical results demonstrate the superiority of our proposed design over benchmark schemes, and also unveil the necessity of the joint design of passive IRS beamforming and active beamforming for achieving better WPCN performance.