In this paper, we propose a DNA storage encoding scheme based on a 64-element coding table combined with forward error correction. The method encodes the data into DNA sequences by LZW compression of the original text, adding error correction codes and scrambling codes. In the encoding process, the effects of GC content limitation and long homopolymers on DNA sequences are considered. At the same time, RS error correction code is introduced to correct the DNA sequence to improve the accuracy of decoding. Finally, the feasibility and effectiveness of the program were verified by simulation experiments on Shakespeare’s sonnets. The data results show that the GC content of DNA sequences encoded by the program is kept at 50%, the homologous multimer length is not more than 2, and the original information can be recovered from the data of 10-fold sequencing depth without error with an error rate of 0.3%. We conducted simulation experiments of primer design, DNA sequence recombination, PCR amplification, and sequence reading on DNA sequences loaded with design information, which further proved the concrete feasibility of the scheme. This scheme provides a reliable and efficient encoding scheme for DNA information storage.