An efficacious and unharmed approach is vital for transmission of sensitive and secret images over unsecure public Internet. In this paper, secured color image compression method based on compressive sampling and Lü system is proposed. Initially, the plain-image is sparsely represented in transform basis. Compressive sampling measurements are obtained from these sparse transform coefficients by employing incoherent sensing matrix. To upgrade the security level, permutation-substitution operations are performed on pixels based on Lü system. To concoct input sensitivity in the scheme, the keys are obtained from input image. Lastly, fast and efficient greedy algorithm is utilized for sparse signal reconstruction. To evaluate the performance of the proposed scheme Peak Signal to Noise Ratio (PSNR), Structural Similarity Index (SSIM), Average Difference (AD), Structural Content (SC), Normalized Cross Correlation (NCC), Normalized Absolute Error (NAE), Edge Strength Similarity (ESSIM), Maximum Difference (MD), Correlation Coefficient, Unified Average Changing Intensity (UACI), Key Sensitivity, Number of pixel change Rate (NPCR), Key Space and Histogram metrics are used. Experimental results demonstrate that the proposed scheme produced highly satisfactory security.