In order to accurately analyze the mechanical properties of composite grains in fiber reinforced composite ceramics (FRCC), a prediction method of composite grain strength is proposed based on the stress concentration effect of nano-interface. On the basis of the microstructure characteristics of FRCC, considering the interaction between nano-fibers, an effective self-consistent method was applied to determine the effective stress field of the nano-interface model. It was assumed that the stress and the displacement between matrix and fiber were continuous at the interface. The uniaxial tension was decomposed into the combination of biaxial tension and pure shear stress by superposition method. The displacement field and the stress field of the matrix and the fiber on the two sides of the interface were obtained according to the displacement function of the FRCC subjected to transverse load, and the stress concentration factor generated by the nano-interface was calculated. Considering the effect of stress concentration caused by dislocation pile-up and nano-interface, a prediction model for fracture stress of composite grains was established, and the influence of the reinforced fiber radius and the volume fraction on the fracture stress was analyzed. Results show that the smaller the radius is, the greater the fracture stress is, and the higher the grain strength becomes. When the radius is larger than 50 nm, it has little effect on the fracture stress. The larger the fiber volume fraction is, the smaller the fracture stress is, and the lower the grain strength becomes.