Abstract: To meet the requirements of mitigating the climate change, a large scale deployment of nuclear energy is expected, which impulses higher efficiency in the utilization of uranium resources. As one of the promising solutions, the integral fast reactor featuring in a high internal breeding can reach a high burn-up, low reprocessing mass, and a long refueling period. In this paper, the relationship between the breeding characteristics and two main design parameters of the core, the rod diameter and the pitch-to-diameter ratio (P/D), was studied. The negative impact on internal breeding caused by the measures for reduction of sodium void reactivity was also analyzed. All calculations were carried out with the Monte Carlo code RMC and ENDF/B-Ⅶ.1 continous-energy ACE data libraries. In each case the breeding characteristics were shown by both breeding ratio of the fissile nuclides and the regeneration ratio of the TRU nuclides. The variation of k_eff, fissile nuclides, TRU nuclides along with burnup were also illustrated. The calculation results indicate that the internal breeding can be significantly enhanced by increasing the rod diameter and by decreasing the P/D. With the current U-Pu-10Zr fuel parameters, a satisfactory burnup reactivity curve can be realized with the rod diameter at 7.0 mm and the P/D at 1.14, taking into account a balance between neutronics and thermal-hydraulics. The positive sodium void reactivity effect makes one of the largest risks of sodium cooled fast reactor (SFR) under unprotected severe accidents. The sodium void reactivity effect can be reduced by setting an upper sodium plenum and reducing the core height-to-diameter ratio (H/D). However, both methods bring significant cost to the internal breeding, due to a higher leakage of neutrons under normal operation. In this paper it is found that to bring the whole-core sodium void reactivity down to zero, the H/D must be as low as 0.15 approximately under the existence of an upper sodium plenum at the height of 40 cm. Such a design results in a fast drop of the burnup reactivity, as well as a low breeding ratio, a low regeneration ratio, and the decreasing of the fissile mass. It can be concluded that in the integral fast reactor design a dilemma exists between the high internal breeding and the low sodium void reactivity effect. This paper suggests that the integral fast reactor should focus on the breeding characteristics and thus a high efficiency of the utilization of uranium resources, leaving the sodium void reactivity to be incorporated into the overall design of the reactor safety features.