To solve the problem of low invisibility and weak anti-attacking ability in the traditional information hiding algorithm, an information hiding algorithm based on compression sensing was proposed. Firstly, the carrier image was operated by first-order GHM (Geronimo Hardin Massopust) multiwavelet transform, and the obtained region in medium energy level was processed by first-order GHM transform again to get HH component, which was decomposed by the Singular Value Decomposition (SVD). Secondly, the secret image was disposed by the wavelet transform, and the obtained wavelet coefficient was processed by compressed sensing in order to get the measurement matrix. Then the elements of the matrix were decomposed by SVD. Finally, the singular value of the carrier image was replaced by the singular value of the secret image to finish the secret information embedding. The experiment shows that compared with existing two information hiding algorithms, the invisibility has been improved by 5.99% and 22.11% respectively; and the robustness against some common attacks such as low-pass filtering, salt and pepper noise, Gaussian noise and JPEG compression has been improved by 4.11% and 11.53% averagely.