A peptide-drug conjugate containing the taxane paclitaxel covalently linked to the proprietary 19 amino acid peptide angiopep-2, in a 3:1 ratio, with potential antineoplastic activity. Upon administration, LRP-1-targeted peptide-drug conjugate GRN1005, via angiopep-2 moiety, binds to LRP-1 (low density lipoprotein receptor-related protein 1), which is highly expressed in blood brain barrier (BBB) and glioma cells. This binding allows the transcytosis of the agent across the BBB and the delivery of the cytotoxic agent paclitaxel. Compared to paclitaxel alone, GRN1005 is able to increase the concentration of paclitaxel in the brain and is also able to specifically deliver paclitaxel to LRP-1-overexpressing tumor cells, both in the brain and in the periphery.