Security is emerging as a critical performance metric for next-generation wireless networks, but conventional multiple-input-multiple-output (MIMO) systems often suffer from severe path loss and are vulnerable to nearby eavesdroppers due to their fixed-antenna configurations. Pinching-antenna systems (PAS) offer a promising alternative, leveraging reconfigurable pinching antennas (PAs) positioned along low-loss dielectric waveguides to enhance channel conditions and dynamically mitigate security threats. In this paper, we propose an artificial noise (AN)-based beamforming scheme for downlink transmissions in PAS, with the goal of maximizing the secrecy rate. A closed-form solution is derived for the single-waveguide scenario, while an alternating optimization approach addresses more complex multiple waveguide setups. Numerical results show that the proposed scheme significantly outperforms conventional MIMO and existing PAS security schemes.