We report the exchange bias in antiferromagnet/ferrimagnet $Cr_2O_3/Fe_3O_4$ core/shell nanoparticles. The magnetic field hysteresis curve for $Cr_2O_3/Fe_3O_4$ nanoparticles after field-cooling (FC) clearly showed both horizontal ($H_{EB}{sim}$610 Oe) and vertical (${Delta}M{sim}$5.6 emu/g) shifts at 5 K. These shifts disappeared as the temperature increased toward the Neel temperature of $Cr_2O_3;(T_N{sim}$307 K). The $H_{EB};and;{Delta}M$ values were sharply decreased between the $1^{st};and;the;2^{nd}$ magnetic field cycles, and then slowly decreased with further cycling. These results are discussed in terms of the formation of single domains with pinned, uncompensated, antiferromagnetic spin and their evolution into multi-domains with cycling.