Dominant features of relaxor ferroelectrics are dielectric dispersion and the nonlinear relationship between reciprocal dielectric constant and temperature. The result of the analysis of the thermal dynamic function for core-shell structure in a grain shows that the core-shell structure doped with dopant in linear gradient descending ingredients can remain high dielectric constant at low temperatures, but cannot lead to the nonlinear relationship between reciprocal dielectric constant and temperature. By comparing diffusion transitions with different doping ingredients, it is suggested that the concentration of ingredient will affect the inhomogeneity of the doping ingredient. A wide distribution of the ingredient between grains by high doping concentration will result in the nonlinear relationship between reciprocal dielectric constant and temperature, and therefore the coexistence of grains in paraelectric phase and in ferroelectric phase in the peak area of dielectric constant. The change of measurement temperature will affect the ratio of the grains in two phases and the change in ferroelectric domains, which results in ferroelectric dielectric dispersion. The core-shell structure will increase the dielectric dispersion. Ferroelectric ceramics, doping species and their concentrations, and sintering temperature all can influence the inhomogeneity of core-shell structure and dielectric dispersion.