Here, a combined molecular modelling methodology was used to identify the binding mode of 4,11-bis((2-guanidinoethyl)amino)anthra[2,3-b]thiophene-5,10-dione (1), a previously reported G4 ligand. After calculating the optimal interaction parameters 1 with the target, two series of tri-armed ligands based on furan- or thiophene-fused anthraquinone scaffolds were designed and synthesized. The new compounds bearing an additional side chain at the 2-position of the heterocycle and the 4,11-side chains with different spacer lengths and structures of terminal groups demonstrated much stronger affinity for telomeric G4 (4-15 times) versus the parental ligand. Moreover, the specificity to the quadruplex over duplex DNA was significantly improved (up to 75 times) when the 3-guanidinopropyl side chain was introduced at the 2-position of the heterocycle ring. All tri-armed ligands demonstrated modest antiproliferative potency, which is likely due to low intracellular penetration. Nevertheless, this work shows how computer-aided rational design of new potent compounds can be used for targeted anticancer therapy.