Human pluripotent stem cells (hPSCs) have the ability to differentiate into cells derived from three germ layers and are an attractive cell source for cell therapy in regenerative medicine. However, hPSCs cannot be cultured on conventional tissue culture flasks but can be cultured on biomaterials with specific hPSC integrin interaction sites. We designed hydrogels conjugated with several designed peptides that had laminin-β4 active sites, optimal elasticities and different zeta potentials. A higher expansion fold of hPSCs cultured on the hydrogels was found with the increasing zeta potential of the hydrogels conjugated with designed peptides, where positive amino acid (lysine) insertion into the peptides promoted higher zeta potentials of the hydrogels and higher expansion folds of hPSCs when cultured on the hydrogels using xeno-free protocols. The hPSCs cultured on hydrogels conjugated with the optimal peptides showed a higher expansion fold than those on recombinant vitronectin-coated plates, which are the gold standard of hPSC cultivation dishes. The hPSCs could differentiate into specific cell lineages, such as mesenchymal stem cells (MSCs) and MSC-derived osteoblasts, even after being cultivated on hydrogels conjugated with optimal peptides for long periods of time, such as 10 passages.