It will reduce the space relativity of original image information and strengthen the randomicity of encrypted information and largely improve the safety of watermarking system if the image had been encrypted during the phase of initializing digital watermarking. Logistic chaotic sequence has been used in shuffling and encrypting the binary image widely, because it sensitively depends upon its initial value and it has the statistical characteristic like which the white noise has. But the original Logistic arithmetic can't encrypt the gray image that can record more information. The paper has designed a new encrypting arithmetic which is based on expanding the bits of mapped sequence and Logistic chaotic sequence. The experiment shows that the new arithmetic is excellent and effective in encrypting the gray image, and also is safer and faster than Arnold arithmetic in encryping the gray image.