Without any surfactant, antiferromagnetic Co3O4 nanoparticles were synthesized successfully for the first time by means of an oxidation-reduction method with cobalt sulfate as starting material, which was oxidized to cobalt salt by NaNO3 after alkalinizing with NaOH. Morphological, structural, spectroscopic and magnetic characterization of the product were done by SEM, TEM, XRD, and VSM, respectively. The average crystallite size (on the base of line profile fitting method), D and sigma, is estimated as 30 +/- 6 nm. Some anomalous magnetic properties and their enhanced effect have been observed in Co3O4 antiferromagnetic nanocrystallftes, including a bias field, coercivity, permanent magnetic moments and an open loop. These phenomena are attributed to the unidirectional anisotropy which is caused by the exchange coupling between AFM and FM layers, the existence of the spin glass like surface spins of Co3O4 nanoparticles due to size effects and surface-area effect.