This paper proposes an encryption scheme for floating probabilistic shaping orthogonal frequency division multiplexing passive optical networks (FPS-OFDM-PON). Four chaotic sequences are generated by the 4D hyperchaotic model for floating probabilistic shaping (FPS) and bubble sort encryption scheme. An experiment is conducted to demonstrate the transmission of a 70Gb/s (7×10Gb/s) FPS-OFDM-PON signal across a 2km weakly coupled 7-core fiber. The keyspace of the 4D hyperchaotic model reaches 10120. The results show that a 1.82 dB gain in receiver sensitivity compared with the conventional uniform 16QAM-OFDM due to the introduction of FPS. When the system is assaulted by an unlawful receiver, the bit error rate (BER) can still remain at 0.49, successfully assuring the system's security. Due to its good transmission and security performance, the scheme has important application prospects in the future optical access network.