We report the grain size effect of hole-doped cobaltite, La(0.88)Sr(0.12)CoO(3), where average sizes are varied from ∼35 to ∼240 nm. The bulk compound is a cluster-glass (CG) compound composed of short range ferromagnetic (FM) clusters embedded in the spin-glass (SG) matrix at low temperature. The short range FM clusters are still retained in the nanocrystalline compound with average size ∼35 nm which are associated with the SG component, displaying CG-like spin dynamics at low temperature. The exchange bias (EB) effect manifested by the shifts in the hysteresis loop is observed due to the field cooling where EB effect is weakened systematically with decreasing grain size. The decrease in the fraction of the FM component is found to be correlated with the weakening of the EB effect with decreasing grain size. Interestingly, the signature of the EB phenomenon due to the field-cooled effect is also evidenced in the temperature as well as the time dependence of resistivity. The grain interior phase separation scenario around the FM/SG interface region has been proposed to interpret the experimental results.