A nanogranular system with inverted ferromagnetic (FM)–antiferromagnetic (AFM) core–matrix morphology is investigated by conducting a modified Monte Carlo Metropolis method. Effects of the AFM- and FM-component ratios on exchange bias field (HE) and coercivity (HC) are presented at low temperature after field cooling, respectively. The sign of HE is negative for weak cooling fields (HFC) but positive for strong ones. The value of HE increases monotonically with the increasing radius of the AFM core (RAF) at the expense of the FM matrix for weak and strong HFC, while it is non-monotonic when HFC is equal to a critical value, which just overcomes the AFM interfacial coupling energy. With the pure increase of the FM dimension, the value of HE decreases firstly and finally levels off at low temperature after cooling in weak or strong HFC. However, HE is around zero and shifts slightly to a positive value for the same critical HFC. The behaviors of HC are independent of HFC. A monotonic decrease of HC with increasing RAF and the opposite trend with increasing FM dimension are both detected in the present system. The phenomena have been interpreted well by analyzing the magnetization reversal and energy competition mechanisms. The increase of RAF stabilizes the magnetic spin configuration of the AFM nanoparticles to contribute to HE, while large numbers of the FM spins may weaken the AFM pinning effect, resulting in the suppression of HE.