Neurodegenerative disorders of the central nervous system are a class of heterogeneous pathologies affecting millions of people worldwide and represent a global health burden in developed and developing countries. Without restorative treatments currently available, research on neuroprotective drugs is considered a health priority. In this study, new analogues of the glycyl-Lprolyl-L-glutamic acid (Glypromate) neuropeptide were designed, synthesized, and biologically evaluated using (1R,3S,4S)-2azanorbornane-3-carboxylic acid as a hybrid construct of L-proline and L-pipecolic acid. Neuroprotection assays carried out in human neuroblastoma SH-SY5Y cells using 6-hydroxydopamine as a stress inducer showed great percentage of recovery (29.7−40.0%) at 100 μM. Among this series, [(1R,3S,4S)-2-glycyl-2-azanorbornane-3-carbonyl]-L-aspartic acid (2a) stands out with a remarkable percentage of recovery (40.0%, at 100 μM) and safe toxicological profile in SH-SY5Y and human adipose mesenchymal stem cells.