Glioblastoma multiforme is the most aggressive primary tumor of the central nervous system. Glioma stem cells (GSCs), a small population of tumor cells with stem-like properties, are supposedly responsible for glioblastoma multiforme relapse after current therapies. In approximately thirty percent of glioblastoma multiforme tumors, telomeres are not maintained by telomerase but through an alternative mechanism, termed alternative lengthening of telomere (ALT), suggesting potential interest in developing specific therapeutic strategies. However, no preclinical model of ALT glioma was available until the isolation of TG20 cells from a human ALT glioma. Herein, we show that TG20 cells exhibit a high level of telomeric recombination but a stable karyotype, indicating that their telomeres retain their protective function against chromosomal instability. TG20 cells possess all of the characteristic features of GSCs: the expression of neural stem cell markers, the generation of intracerebral tumors in NOD-SCID-IL2Rγ (NSG) mice as well as in nude mice, and the ability to sustain serial intracerebral transplantations without expressing telomerase, demonstrating the stability of the ALT phenotype in vivo. Furthermore, we also demonstrate that 360B, a G-quadruplex ligand of the pyridine derivative series that impairs telomere replication and mitotic progression in cancer cells, prevents the development of TG20 tumors. Together, our results show that intracerebral grafts of TG20 cells in immunodeficient mice constitute an efficient preclinical model of ALT glioblastoma multiforme and that G-quadruplex ligands are a potential therapy for this specific type of tumor.