Telomerase, a reverse transcriptase enzyme, is found to over express in most cancer cells. It elongates the telomere region by repeated adding of TTAGGG in the 3′-end and leads to excess cell proliferation which causes cancer. G-quadruplex (G4) formation can inhibit such telomere lengthening. So, stabilization of G4 structure as well as inhibition of telomerase activity is very promising approach in targeted cancer therapy. Herein, the aptitude of a synthetic dendritic peptide, C^δ2–(YEE)–E (peptide 1), to target specifically the human telomeric G4 DNA, dAGGG(TTAGGG)₃, has been evaluated. Both biochemical and biophysical techniques including gel mobility shift assay, isothermal titration calorimetry and fluorescence spectroscopy have been employed for the purpose. Circular dichroism study reveals that the targeting results an increase in thermal stability of G4 DNA. Interestingly, replacement of N-terminal tyrosine residue of peptide 1 by valine, C^δ2–(VEE)–E, (peptide 2) consequences in loss of its G4 DNA targeting ability, although both the peptides exhibit comparable affinity toward double-stranded DNA. Of note, peptide 1 causes cessation of growth of human cancer cells (HeLa and U2OS) and induces apoptosis in vitro. But it has no significant inhibitory effect on the growth of normal human embryonic kidney 293 cells. Mechanistically, Telomeric Repeat Amplification Protocol (TRAP) assay indicates that peptide 1 effectively inhibits the telomerase activity in human cell extracts. Overall, this study demonstrates the usefulness of a synthetic dendritic peptide as an inhibitor of tumor cell growth by inducing apoptosis upon targeting the telomeric G4 DNA.