By use of the single-molecule observation, we count the number of DNA double-strand breaks caused by γ-ray irradiation with genome-sized DNA molecules (166 kbp). We find that P1, the number of double-strand breaks (DSBs) per base pair per unit Gy, is nearly inversely proportional to the DNA concentration above a certain threshold DNA concentration. The inverse relationship implies that the total number of DSBs remains essentially constant. We give a theoretical interpretation of our experimental results in terms of attack of reactive species upon DNA molecules, indicating the significance of the characteristics of genome-sized giant DNA as semiflexible polymers for the efficiency of DSBs.