Chaotic optical communication has recently garnered considerable research interest for providing physical layer security. In this work, we propose and demonstrate a secure space-division-multiplexing (SDM) system based on multi-channel chaos random en/decryption with remotely synchronized Fabry-Perot (FP) lasers. By a random combination of multi-longitudinal modes from the FP lasers, multi-channel low-correlated chaotic signals can be produced and then utilized for encrypting the confidential data, which effectively provides multiple possibilities of optical encryption from a single chaotic laser source. As a proof-of-principle demonstration in a multi-core fiber-based SDM system, 28 Gb/s/core on-off keying (OOK) and 64 Gb/s/core quadrature phase-shift keying (QPSK) signals are successfully encrypted and securely transmitted over a 10 km seven-core fiber. The demonstrated scheme may provide a new way for a physical-layer secure SDM system with enhanced capacity and security.