In this paper, a new image encryption algorithm employing the combination of chaos and cellular automata is proposed. The proposed algorithm consists of both permutation and diffusion stages. While the permutation process is carried out using logistic map and Conway's game-of-life cellular automata, the diffusion process is carried out using Chebyshev map and Lorenz equation. Further, a complex matrix generated from the plain image is used as an additional component in the diffusion process, which enables the encrypted image to exhibit a strong sensitivity to the input image. The proposed algorithm has been tested with various input images, and the performance is compared with other existing algorithms. The performance metrics obtained on the developed algorithm such as high key space, ideal number of pixels change rate and unified average changing intensity values, and very less correlation among the adjacent pixels demonstrate the high effectiveness and security features of the proposed algorithm.