A new two-dimensional chaotic system in the form of a cascade structure is designed, which is derived from the Chebyshev system and the infinite collapse system. Performance analysis including trajectory, Lyapunov exponent and approximate entropy indicate that it has a larger chaotic range, better ergodicity and more complex chaotic behaviour than those of advanced two-dimensional chaotic system recently proposed. Moreover, to protect the security of the crowd image data, the newly designed two-dimensional chaotic system is utilized to propose a visually meaningful image cryptosystem combined with singular value decomposition and Bernstein polynomial. First, the plain image is compressed by singular value decomposition, and then encrypted to the noise-like cipher image by scrambling and diffusion algorithm. Later, the steganographic image is obtained by randomly embedding the cipher image into a carrier image in spatial domain through the Bernstein polynomial based embedding method, thereby realizing the double security of image information and image appearance. Besides, the visual quality of the steganographic image can be improved by the adjustment factor according to different carrier images during the embedding process. Ultimately, security analyses indicate that it has higher encryption efficiency (2 Mbps) and the visual quality of steganography image can reach 39 dB.