In order to improve the performance of image compression so as to achieve better lossless image compression, a lossless image compression method based on wavelet transform and arithmetic coding is proposed in this paper. First of all, this method performs integer wavelet transform on all the highfrequency and lowfrequency components of the image. Then, the parameters of the finite mixture model with geometric distribution are estimated by using the expectation maximization algorithm and the maximum likelihood estimation. Finally, the arithmetic coding is completed by the method of histogram truncation. The test results of multiple sets of image data show that compared with other methods, the proposed compression method has better compression performance (subjective and objective fidelity index), i.e., higher compression ratio and peak signaltonoise ratio.