In this paper, an efficient and robust meaningful image encryption (MIE) scheme is developed by combining block compressive sensing (BCS) and singular value decomposition (SVD) embedding. This work devotes to the balanced performance of security, compression, robustness and running efficiency. First, the plain image is divided equally and sparsely represented in discrete cosine transform (DCT) domain, and the coefficient vectors are confused using the coefficient random permutation (CRP) strategy and encrypted into a secret image by compressive sensing. Next, SVD embedding is employed to embed the secret image into a carrier image to create the final meaningful cipher image. In pursuit of superior security, the hyper-chaotic Lorenz system is utilized to generate the updated secret code streams for encryption and embedding with assistance from the counter mode. This scheme is suitable for processing the medium and large images in parallel. Additionally, it exhibits superior robustness and efficiency compared with existing related schemes. Simulation results and comprehensive performance analyses are presented to demonstrate the effectiveness, secrecy and robustness of the proposed scheme.