A mechanical model for the strength prediction of composite ceramics (CC) with nano-interface and micro-interface is presented based on nano-interface damage mechanism and micro-interface damage mechanism. Firstly, on the basis of composite microstructure, micro-domain whose main component is regularly arranging eutectic crystal is built. Moreover, nano-cell is brought into eutectic crystal which is comprised of parallel inclusions, nano-interfaces, matrix and effective medium. Secondly, the stress field of micro-domain is deduced based on interaction direct derivative. Thirdly, three failure mechanisms of micro-domain including the fracture of eutectic crystal based on the damage of nano-interface, the slipping and cracking of micro-interface among eutectic crystals are taken into account. Finally, the strength model of the composite ceramic is obtained by using random distribution of the micro-domain, and several factors that may decrease the strength of the composite ceramic are analyzed. The results indicate that inclusion size, volume fraction and micro-interface cracking size are the three primary factors decreasing the strength of composite, while the shapes of inclusion and structure of domain have little influence on the strength of composite. The comparison with experimental data shows that the model is effective in the explanation of the failure mechanism of composite ceramic with nano-interface and micro-interface. [GRAPHICS] .