By using Monte Carlo simulation on a ferromagnetic core/antiferromagnetic shell nanoparticle, we investigate in details the exchange bias of the magnetic hysteresis as a function of both core radius and shell thickness, at low temperature. It is found that the exchange bias is very sensitive to the core radius and a small variation of the radius may lead to a big fluctuation of the bias. In a general tendency the exchange bias is enhanced by increasing shell thickness and decreasing core radius. The intrinsic correlation between the exchange bias and the spin configuration on the core-shell interface is demonstrated. We further investigate the dependence of the exchange bias on temperature and random field inside the nanoparticle, indicating a monotonous decreasing of the bias with the magnitude of random field and temperature, respectively.