Core-shell nanoparticles of MnO|Mn3O4 with average particle sizes of 5-60 nm, composed of an antiferromagnetic (AFM) core and a ferrimagnetic (FiM) shell, have been synthesized and their magnetic properties investigated. The core-shell structure has been generated by the passivation of the MnO cores, yielding an inverted AFM-core|FiM-shell system, as opposed to the typical FM-core|AFM-shell. The exchange-coupling between AFM and FiM gives rise to an enhanced coercivity of approximately 8 kOe and a loop shift of approximately 2 kOe at 10 K, i.e., exchange bias. The coercivity and loop shift show a non-monotonic variation with the core diameter. The large coercivity and the loop shift are ascribed to the highly anisotropic Mn3O4 and size effects of the AFM (i.e., uncompensated spins, AFM domains, and size-dependent transition temperature).