Telomeres carry important biological functions such as the protection of chromosomes. In this paper, we have developed a fluorescence anisotropy imaging system for monitoring DNA digestion inside live cells. The nuclease-resistant capability of telomere-like ssDNAs in nuclei of human breast cancer cells is studied. We found that those oligonucleotides were clearly more stable than regular DNA sequences during the time course of the experiments. We conclude that the G-quadruplex structure of the telomere-like ssDNA makes it inherently more stable in intracellular environments than non-G-quadruplex structures. This will help us understand why the G-quadruplex forming telomere sequences were adopted by almost all eukaryotic cells to protect the ends of chromosomes. This is the first time such a phenomenon was observed in live cells. Our fluorescence anisotropy imaging provides an efficient way to directly monitor DNA digestion in any region of live cells in real time, providing insights into many important and related intracellular processes.