In this study, the microwave-assisted copper(I)-catalyzed 1,3-dipolar cycloaddition reaction was used to synthesize peptide triazole-based polymers from two novel peptide-based monomers: azido-phenylalanyl-alanyl-lysyl-propargyl amide (1) and azido-phenylalanyl-alanyl-glycolyl-lysyl-propargyl amide (2). The selected monomers have sites for enzymatic degradation as well as for chemical hydrolysis to render the resulting polymer biodegradable. Depending on the monomer concentration in DMF, the molecular mass of the polymers could be tailored between 4.5 and 13.9 kDa (corresponding with 33-100 amino acid residues per polymer chain). As anticipated, both polymers can be enzymatically degraded by trypsin and chymotrypsin, whereas the ester bond in the polymer of 2 undergoes chemical hydrolysis under physiological conditions, as was shown by a ninhydrin-based colorimetric assay and MALDI-TOF analysis. In conclusion, the microwave-assisted copper(l)-catalyzed 1,3-dipolar cycloaddition reaction is an effective tool for synthesizing biodegradable peptide polymers, and it opens up new approaches toward the synthesis of (novel) designed biomedical materials.