To understand the formation of core-shell structure in $BaTiO_3$ (BT) grains in multilayer ceramic capacitors, specimens were prepared with BT powders mixed with Y and Mg, and their microstructures were investigated with scanning electron microscopy, x-ray diffractometry, and transmission electron microscopy. Microstructural investigation showed that Y dissolved easily in BT lattice to a certain depth inside of the grain, whereas Mg tended to stay at grain boundaries rather than become incorporated into BT. It was considered that in case of Y and Mg addition in a proper ratio, Y could play a dominant role in the formation of shell leading to a slight dissolution of Mg in the shell. Next, the effects of ball-milling conditions on the core-shell formation were studied. As the ball-milling time increased, the milled powders did not show a significant change in size distribution but rather an increase of residual strain, which was attributed to the milling damage. The increase in milling damage facilitated the shell formation, leading to the increased shell portion in the core-shell grain.