This paper address the issue of image compression and encryption is to minimize the amount of data required to represent the images and to provide better privacy and security to the users. A joint lossless algorithm: Integer Wavelet Transform (IWT) with hybrid hyperchaotic system is proposed to enhance the security of data transmission. IWT is used to compress the images and then the encryption is performed by hybrid hyper chaotic system. A hybrid hyperchaotic system: Fractional Order Hyperchaotic Cellular Neural Network (FOHCNN) and Fractional Order Four Dimensional Modified Chua’s Circuit (FOFDMCC) is used to generate the pseudorandom sequences. The pixel substitution and scrambling is realized by Global Bit Scrambling (GBS) that improves the cipher unpredictability. In this study, Deoxyribonucleic Acid (DNA) sequence is adopted instead of binary operation that resists the cipher images from crop attack, differential attack and salt and pepper noise. In the experimental phase, the proposed algorithm showed good performance in encryption compared to existing algorithms.