As the current data encryption algorithms lack covertness, a visually secure image encryption algorithm is proposed, which combines the P-tensor product compressive sensing (PTP-CS) model and the new segmented chaotic map (SCM). First, the new SCM with fractional structure is designed according to the “stretching and squeezing” mechanism to construct the key-controlled measurement matrix. Secondly, under the joint control of the measurement matrix and cipher code streams, the intermediate secret image without visual semantics is generated after the two-dimensional (2D) Arnold scrambling, linear measurement, and bidirectional XOR diffusion of the plaintext wavelet-packet coefficient matrix. Then, the digital steganographic coding approach is employed to embed it stochastically into the non-secret-involved transmission medium to synchronously protect the content and appearance of the sensitive plaintext data. Simulation experiments and security analysis indicate that the proposed encryption algorithm is capable of defending against various common attacks, and it has good visual security and compression performance.