Disclosed are the anti-bacterial activity and the anti-tumor activity of a class of new spiro three-membered ring and spiro five-membered ring peptide deformylase inhibitor. The spiro three-membered ring and spiro five-membered ring peptide deformylase inhibitor of the present invention, as a class of new anti-bacterial agent, are effective against many antibiotic-resistant Gram-positive strains by inhibiting the activity of the peptide deformylase required in the synthesis of bacterial proteins, and do not affect the synthetic process of the main proteins of the human body, thus selectively killing bacteria. The spiro three-membered ring and spiro five-membered ring peptide deformylase inhibitor of the present invention, as a class of new anti-bacterial agent, can affect the energy balance of the cancer cells through inhibiting the peptide deformylase of the mitochondria in the cells, so that the mitochondrial membrane is depolarized, ATP is exhausted and cell apoptosis is promoted, and has good inhibitory activities on many cancer cell strains such as colorectal cancer, leukemia, lung cancer, gastric cancer, cervical cancer, breast cancer, prostatic cancer, liver cancer and osteosarcoma at relatively lower concentrations. The structure of exemplary invention spiro three-membered ring and spiro five-membered ring peptide deformylase inhibitors are represented by one or more of: