Driven by the development of multimedia, the encryption of multimedia digital audio has received more attention; however, cryptography-based encryption methods have many shortcomings in encryption of multimedia information, and new encryption methods are urgently needed. This paper briefly introduced cryptography and chaos theory, designed a chaos-based encryption algorithm that combined Logistic mapping and Sine mapping for confusion and used a Hopfield chaos neural network for diffusion, explained the encryption and decryption process of the algorithm, and tested the algorithm. It was found that the keys obtained by the proposed algorithm passed the SP800-22 test, and the correlation between the three encrypted audio and the original audio was 0.0261, -0.0536, and 0.0237, respectively, all of which were small, and the peak signal-to-noise ratio (PSNR) values were -0.348 dB, -7.645 dB, and -3.636 dB, respectively, which were significantly different from the original audio. The NSCR and UACI were also closer to the original values. The results prove that the proposed algorithm has good security and can encrypt the actual multimedia digital audio.