This paper investigates physical layer security (PLS) for a movable antenna (MA)-assisted full-duplex (FD) system. In this system, an FD base station (BS) with multiple MAs for transmission and reception provides services for an uplink (UL) user and a downlink (DL) user. Each user operates in half-duplex (HD) mode and is equipped with a single fixed-position antenna (FPA), in the presence of a single-FPA eavesdropper (Eve). To ensure secure communication, artificial noise (AN) is transmitted to obstruct the interception of Eve. The objective of this paper is to maximize the sum secrecy rate (SSR) of the UL and DL users by jointly optimizing the beamformers of the BS and the positions of MAs. This paper also proposes an alternating optimization (AO) method to address the non-convex problem, which decomposes the optimization problem into three subproblems and solves them iteratively. Simulation results demonstrate a significant performance gain in the SSR achieved by the proposed scheme compared to the benchmark schemes.