For the problem of the leakage current of single-phase transformerless photovoltaic grid-connected inverters, the topology evolution of the transformerless half-bridge type and full-bridge type is derived and a bridge-type topology evolution network is established. The topology characteristics of single-phase transformerless photovoltaic grid-connected inverter are analyzed. This paper presents some of the single-phase transformerless photovoltaic grid-connected inverter topology and discusses the evolution rules among various topologies to clarify the interrelationship between topologies. A new topology is deduced by using the evolution rules to further prove it. Finally, the validity of the leakage current suppression function of the proposed new topology and correctness of the evolution rules are verified by PSIM.