A visually meaningful image encryption algorithm is presented. More specifically, a strategy of M-ary decomposition is first presented to be used to represent a positive integer in multi base. Then the concept of virtual bits is presented and the relationship between it and the M-ary decomposition is discussed. Based on the M-ary decomposition strategy, a non-standard image pre-encryption algorithm is proposed where each pixel value of the pre-encrypted image is limited to a specified range thus saving a small amount of virtual bits which can also be used to improve the visual quality of cipher images. A Generalized Embedding Model is proposed, where the Generalized-LSB (G-LSB) method is used to embed virtual bits into the host domain and an error-correcting strategy is also presented. The optimal static virtual embedded bits (SVEB) are found and a set of rules for dynamic virtual embedded bits (DVEB) are constructed. Experimental simulations show that the visual quality of cipher images is better than that using existing visually meaningful image encryption algorithms.