The electrical property and microstructure in $BaTiO_3$ ceramics doped rare-earth ions with intermediate ionic size ($Dy^{3+},Ho^{3+},Y^{3+}$) were investigated. Microstructures have been characterized using scanning electron microscopy (SEM), transmission electron microscopy (TEM) and X-ray diffraction (XRD). Incorporation of rare-earth ions to $BaTiO_3$ ceramics depended on their ionic radius sensitively. Compared to Ho and Y ions, Dy ions provide $BaTiO_3$ ceramics with the high rate of densification and well-developed shell formation, due to their high solubility in the $BaTiO_3$ lattice, but the microstructure of Dy doped $BaTiO_3$ ceramics is unstable at high temperature, because Dy ions could not play a role of grain growth inhibition, leading to diffuse into $BaTiO_3$ lattice continuously after completion of densification during sintering. Comparing electrical property and microstructure, it is shown that the reliability of capacitor improved by high shell ratio.