To ensure the security issues of information transmission in modern network, a double encryption algorithm of computer generated hologram based on compressed sensing theory and block Arnold transformation scrambling has been proposed. The phase-only hologram of original image has been produced, the hologram has been encrypted by using the random measurement matrix of compressed sensing as a key. It has been encrypted again by block Arnold transformation scrambling. The image after two-time encryption can be decrypted by using the keys and reproduce the original one. Compare to conventional optical holographic encryption, this method has a more flexible design, simple optical path and the two encryptions both have randomness, so it improves the security of information transmission greatly. Result shows that the decryption image is ideal, safe and robust. The proposed method is verified by building a holographic display system based on silicon liquid crystal spatial light modulator.