Physical layer security (PLS) technology based on the fixed-position antenna (FPA) has {attracted widespread attention}. Due to the fixed feature of the antennas, current FPA-based PLS schemes cannot fully utilize the spatial degree of freedom, and thus a weaken secure gain in the desired/undesired direction may exist. Different from the concept of FPA, mobile antenna (MA) is a novel technology that {reconfigures} the wireless channels and enhances the corresponding capacity through the flexible movement of antennas on a minor scale. MA-empowered PLS enjoys huge potential and deserves further investigation. In this paper, we, for the first time, investigate the secrecy performance of MA-enabled PLS system where a MA-based Alice transmits the confidential information to multiple single-antenna Bobs, in the presence of the single-antenna eavesdropper (Eve) {in the absence} of perfect channel state information (CSI). For the purpose of the secrecy rate maximization of the worst Bob, we jointly design the transmit beamforming and antenna positions at the Alice, subject to the minimum moving distance of the antenna, uncertainty CSI of Eve, and maximum transmit power. Furthermore, the projected gradient ascent (PGA), alternating optimization (AO), and simulated annealing (SA) {are} adopted to solve the non-convex characteristics of the problem of the secrecy rate maximization. Simulation results demonstrate the effectiveness and correctness of the proposed method. In particular, MA-enabled PLS scheme can significantly enhance the secrecy rate compared to the conventional FPA-based ones for different settings of key system parameters.