The first part of my project was the study of the hyperbranched polymers toward catalysis. Hyperbranched polymers possessing iron porphyrin cores were synthesized successfully with even core distribution. These iron porphyrin cored hyperbranched polymers are utilized to mimic natural enzyme- Cytochrome P450. In the terminal alkene epoxidation, these hyperbranched polymer catalysts showed obvious stability increase. In the selectivity experiment, hyperbranched polymer catalysts did not display great shape selectivity as dendrimer catalysts which could be reason from their loose and flexible structure.