Different species of Leishmania can cause a variety of medically important diseases, whose control and treatment are still health problems. Telomere binding proteins (TBPs) have potential as targets for anti-parasitic chemotherapy because of their importance for genome stability and cell viability. Here, we describe LaTBP1 a protein that has a Myb-like DNA-binding domain, a feature shared by most double-stranded telomeric proteins. Binding assays using full-length and truncated LaTBP1 combined with spectroscopy analysis were used to map the boundaries of the Myb-like domain near to the protein only tryptophan residue. The Myb-like domain of LaTBP1 contains a conserved hydrophobic cavity implicated in DNA-binding activity. A hypothetical model helped to visualize that it shares structural homology with domains of other Myb-containing proteins. Competition assays and chromatin immunoprecipitation confirmed the specificity of LaTBP1 for telomeric and GT-rich DNAs, suggesting that LaTBP1 is a new TBP.