Digitized images are used widely in current industrial applications; however, digital images cost a huge storage capacity, leading to transmission bandwidth constraints. Therefore, an image compression technique was developed to solve this drawback. Differential pulse code modulation (DPCM) is the most widely used method among predictive image coding schemes. It is based on the notation of quantizing a prediction error signal after the prediction operation to reduce the original data complexity. The design of the predictor influences the performance of the whole DPCM. Therefore, the predictor constitutes a central topic in the DPCM system. We make efforts toward the design of a predictor by using a genetic algorithm (GA). By the operations of crossover and mutation, several predictor coefficients are yielded after hundreds of generations. The predictor generated by the GA outperforms the current eight different predictive schemes in Joint Photographic Experts Group lossless (JPEG-LS) still image compression standard. Because the JPEG-LS compression scheme is currently the most widely used lossless compression method, our results contribute to the applications of compression.