Cytosolic protein delivery is a prerequisite for the development of protein therapeutics that act on intracellular targets. Proteins are generally membrane-impermeable and thus need a carrier such as a polymer to facilitate their internalization. However, the efficient binding of proteins with different isoelectric points to polymeric carriers is challenging. In this study, we designed a coordinative dendrimer to solve this problem. The dendrimers modified with dipicolylamine/zinc(II) complex were capable of binding proteins through a combination of ionic and coordination interactions. The best polymer efficiently delivered 30 cargo proteins and peptides into the cytosol, while maintaining their bioactivity after intracellular release. The removal or replacement of zinc ions in the polymer with other transition-metal ions lead to significantly decreased efficiency in cytosolic protein delivery. This study provides a new strategy to develop robust and efficient polymers for cytosolic protein delivery.