We report unusual cooling field dependence of the exchange bias in oxide-coated cobalt nanoparticles embedded within the nanopores of a carbon matrix. The size-distribution of the nanoparticles and the exchange bias coupling observed up to about 200 K between the Co-oxide shell (∼3-4 nm) and the ferromagnetic Co-cores (∼4-6 nm) are the key to understand the magnetic properties of this system. The estimated values of the effective anisotropy constant and saturation magnetization obtained from the fit of the zero-field cooling and field cooling magnetization vs. temperature curves agree quite well with those of the bulk fcc-Co.