In this paper, we investigate finite mixture models (FMM) and adaptive arithmetic coding (AAC) for block-based lossless image compression. The AAC performance depends on how well the model fits the source symbols' statistics. In addition, when encoding small block, the number of source symbols is considerably large by comparison with the number of samples in that block, which results in a loss of compression efficiency. To this end, we propose to model each block with an appropriately FMM by maximizing the probability of samples that belong to that block. The mixture parameters are estimated through maximum likelihood using the Expectation-Maximization (EM) algorithm in order to maximize the arithmetic coding efficiency. The comparative studies of some particular test images prove the efficiency of the mixture models for lossless image compression. The experimental results show significant improvements over conventional adaptive arithmetic encoders and the state-of-the-art lossless image compression standards and algorithms.