Today, social communication through the Internet has become more popular and has become a crucial part of our daily life. Naturally, sending and receiving various data through the Internet has also grown a lot. Keeping important data secure in transit has become a challenge for individuals and even organizations. Therefore, the trinity of confidentiality, integrity, and availability will be essential, and encryption will definitely be one of the best solutions to this problem. Of course, for image data, it will not be possible to use conventional encryption methods for various reasons, such as the redundancy of image data, the strong correlation of adj acent pixels, and the large volume of image data. Therefore, special methods were developed for image encryption. Among the prevalent methods for image encryption is the use of DNA sequences as well as chaos signals. In this paper, a cycling 3D chaotic map and DNA sequences are used to present a new method for color image encryption. Several experimental analyses were performed on the proposed method, and the results proved that the presented method is secure and efficient.