Recently, many image encryption schemes have been developed using Latin squares. When encrypting a color image, these algorithms treat the color image as three greyscale images and encrypt these greyscale images one by one using the Latin squares. Obviously, these algorithms do not sufficiently consider the inner connections between the color image and Latin square and thus result in many redundant operations and low efficiency. To address this issue, in this paper, we propose a new color image encryption algorithm (CIEA) that sufficiently considers the properties of the color image and Latin square. First, we propose a two-dimensional chaotic system called 2D-LSM to address the weaknesses of existing chaotic systems. Then, we design a new CIEA using orthogonal Latin squares and 2D-LSM. The proposed CIEA can make full use of the inherent connections of the orthogonal Latin squares and color image and executes the encryption process in the pixel level. Simulation and security analysis results show that the proposed CIEA has a high level of security and can outperform some representative image encryption algorithms.