Surveillance performance is studied for a wireless eavesdropping system, where a full-duplex legitimate monitor eavesdrops a suspicious link efficiently with the artificial noise (AN) assistance. Different from the existing work in the literature, the suspicious receiver in this paper is assumed to be capable of detecting the presence of AN. Once such receiver detects the AN, the suspicious user will stop transmission, which is harmful for the surveillance performance. Hence, to improve the surveillance performance, AN should be transmitted covertly with a low detection probability by the suspicious receiver. Under these assumptions, an optimization problem is formulated to maximize the eavesdropping non-outage probability under a covert constraint. Based on the detection ability at the suspicious receiver, a novel scheme is proposed to solve the optimization problem by iterative search. Moreover, we investigate the impact of both the suspicious link uncertainty and the jamming link uncertainty on the covert surveillance performance. Simulations are performed to verify the analyses. We show that the suspicious link uncertainty benefits the surveillance performance, while the jamming link uncertainty can degrade the surveillance performance.