Deoxyribonucleic acid (DNA) is an important bio-macromolecule. DNA double strand breaks (DSBs) are considered to be the most important initial damage responsible for all biological effects induced by ionizing radiation. In this paper the length distribution of DNA fragments induced by 7Li ionizing radiation is fitted with the random breakage model. In this model, the parameter u is the average number of DSBs on every DNA molecule induced by ionizing radiation. The fitting result shows that the random breakage model cannot describe the distribution of DNA fragments in lower doses, while the random breakage model is in better accordance with the experimental data in higher doses. It is shown that the length distribution of DNA fragments has random statistical feature in higher doses. In this situation, the random breakage model looks like a model without any parameter since the u has specific physical meaning and can directly be obtained from experimental data.