In this paper, a lossless image compression and encryption algorithm combining JPEG-LS, neural networks and hyperchaotic mapping is proposed to protect the privacy of digital images and reduce data storage space. Firstly, we design a new 2-Dimensional Logistic-Like Hyperchaotic Map (2DLLHM), which has more complex dynamics than some existing known chaotic systems, and can be used to build a good pseudorandom sequence generator. Secondly, to compress images efficiently, we design a new pixel predictor by combining the MED (Median Edge Detector) ...