Human telomere consists of tandem repeats of guanines; thus, it can form an intramolecular G-quadruplex structure, which can inhibit the telomerase enzyme that is found active in more than 85% of cancer cells. The present work investigated the interactions of GW2974, a quinazoline derivative with telomeric G-quadruplex AG3(TTAGGG)3. GW2974 had shown a good affinity to G-quadruplex DNA with a binding constant of 2.41 × 106 M−1 and melting temperature shift ΔTm of 9.9 °C. Increasing the GW2974 ratio with DNA up to five times showed an inverse effect on G-quadruplex DNA stability. The stoichiometric ratio between GW2974 and TelQ (per strand) was 2:1. Results obtained from absorption, fluorescence, and CD spectroscopic techniques indicated that GW2974 interacted with G-quadruplex through different binding modes. GW2974 showed good specificity to quadruplex over duplex DNA by 4.71-fold. These results indicated that stabilizing of telomeric G-quadruplex inhibited telomerase enzyme, which could be a potential anticancer mechanism of GW2974.