The security of digital images is becoming increasingly important due to the widespread use of image transmission through networks. Therefore, encryption is necessary to protect the confidentiality and integrity of digital images. In this paper, a new digital image encryption algorithm is proposed by combining multiple Hill ciphers, unimodular matrix, and logistic map. The proposed algorithm can improve the security of the image encryption process by introducing multiple encryption layers. The unimodular matrix is used to shuffle the image pixels and the logistic map is used to generate the encryption keys. The performance of the proposed algorithm is evaluated by applying it to various types of digital images. The experimental results show that the proposed algorithm can achieve high-level security. Moreover, the proposed algorithm has a faster encryption time compared to other existing image encryption algorithms. Therefore, it is a promising algorithm for digital image encryption applications that require high security and fast processing time.