In this letter, we consider a unmanned-aerial-vehicle (UAV)-aided millimeter-wave (mmWave) wireless system and present a covert transmission design from the mmWave-UAV (Alice) to a legitimate ground user (Bob), subject to detection attack by a third party (Willie). Of particular interest is that Alice has no knowledge of both Bob and Willie’s exact locations, which are deemed to be difficult to estimate in practice. As a result, Alice opts for a time-division based beam-sweeping transmission scheme to enable opportunistic communication to Bob. An average throughput maximization problem is formulated that jointly optimizes the number of beams, transmit power and flight altitude of Alice, by taking into account the statistical location distribution of Bob and a covertness constraint on Willie. To solve this highly non-concave problem that involves a stochastic objective function, we exploit the minorization-maximization method, transform the problem into a series of simple approximation problems and then develop a batch stochastic minorization-maximization (BSM) algorithm. Numerical results confirm the effectiveness of the BSM algorithm and demonstrate important tradeoff among the key design parameters considered.