Among the known breast cancers, the subtype with HER2 receptors-overexpressing cells is associated with a poor prognosis. The adopted monoclonal antibody Trastuzumab has improved clinical outcomes, but it is associated with drug resistance and relatively high costs. The present work adopted the peptide solid-phase synthesis method to synthesise branched poly(ε-lysine) peptide dendrons with 8 branching arms integrating, at their carboxy terminal molecular root, either an arginine or the HER2 receptor-binding sequence LSYCCK or the scramble sequence CSCLYK. These dendrons were synthesised in quantities higher than 100 mg/batch and with a purity exceeding 95%. When tested with two types of breast cancer cells, the dendrons led to levels of inhibition in the HER2 receptor-overexpressing breast cancer cells (SKBR3) comparable to Trastuzumab and higher than breast cancer cells with low receptor expression (MDA-MB-231) where inhibition was more moderate. Noticeably, the presence of the amino acid sequence LSYCCK at the dendron molecular root did not appear to produce any additional inhibitory effect. This was demonstrated also when the scramble sequence CSCLYK was integrated into the dendron and by the lack of any antiproliferative effect by the control linear target sequence. The specific inhibitory effect on proliferation was finally proven by the absence of cytotoxicity and normal expression of the cell migration marker N-Cadherin. Therefore, the present study shows the potential of poly(ε-lysine) dendrons as a cost-effective alternative to Trastuzumab in the treatment of HER2-positive breast cancer.