We have carried out systematic studies on well-characterized monodisperse Fe 3 O 4 /γ-Fe 2 O 3 core/shell nanoparticles of 2–30 nm having a very narrow size distribution and possessing a uniquely mono-layer of surface γ-Fe 2 O 3 . This unique core-shell structure, probably having a disordered magnetic surface state, leads us to three key observations of unusual magnetic properties: i) a very large magnetic exchange anisotropy reaching over 7 × 10 6 erg/cm 3 for the smaller particles, ii) exchange bias behavior in the magnetization data of the core/shell Fe 3 O 4 /γ-Fe 2 O 3 nanoparticles, and iii) the temperature dependence of the coercive field following an unusual exponential behavior.