In this paper, the authors present an image encryption and compression system, where encryption of an image is conducted prior to compression. The proposed image encryption operated in the prediction error domain is to provide a reasonably high level of security. Also an efficient lossless compression of the encrypted image is performed by using arithmetic coding with run length encoding. They achieved higher compression ratios by using arithmetic coding with run length encoding compared to using only arithmetic coding algorithm. Experimental results illustrated that the proposed system is efficient in terms of compression ratio and peak signal to noise ratio.