In this letter, we propose to employ movable antenna (MA) to enhance covert communications with noise uncertainty, where the confidential data is transmitted from an MA-aided access point (AP) to multiple users with a warden attempting to detect the existence of the legal transmission. To maximize the sum rate of users under covertness constraint, we formulate an optimization problem to jointly design the transmit beamforming and the positions of MAs at the AP. To solve the formulated non-convex optimization problem, we develop a block successive upper-bound minimization (BSUM) based algorithm, where the proximal distance algorithm (PDA) and the successive convex approximation (SCA) are employed to optimize the transmit beamforming and the MAs' positions, respectively. Simulation results show that the proposed MAs-aided system can significantly increase the covert sum rate via antenna position optimization as compared to conventional systems with fixed-position antennas (FPAs).