In order to solve the problems in the existing chaotic image encryption algorithms， such as the weak chaotic property and low security of low-dimensional chaotic systems， the high transmission cost and large storage space of high-dimensional chaotic systems， as well as the large occupied space and high transmission cost of traditional measurement matrices in compressed sensing technology， this paper proposed a color image encryption algorithm combining dual hyperchaotic systems with compressed sensing and Fibonacci transformation. Firstly， the Arnold algorithm was optimized through the Lorenz hyperchaotic system to improve security. Secondly， the measurement matrix of compressed sensing was improved by using the 6D hyperchaotic system to reduce space resources and transmission costs. Thirdly， scrambling was performed using the 6D hyperchaotic system with a large key space and high security to enhance security. Finally， the Fibonacci Q matrix was used for block diffusion to enhance unpredictability. In addition， the 2D projection gradient embedding decryption algorithm was introduced in image reconstruction. Compared with the traditional reconstruction algorithm， it had higher security and computational efficiency. Experimental results show that the information entropy exceeds 7.999， which is closer to the ideal value of 8， the correlation coefficient is close to 0， the rate of pixel number change and the uniform change rate are close to the ideal values of 99.609 4% and 33.463 5%. While effectively protecting the security and integrity of the image， it has strong resistance to statistical attacks and differential attacks as well as better robustness.