The study of topological photonics is of great significance in the field of optical communication. In order to achieve topological edge states (TESs) and corner states (TCSs), a two-dimensional square photonic crystal structure was constructed based on the Su-Schrieffer-Heeger (SSH) model. The energy bands of the structure were simulated and calculated using finite element software, and the corresponding modes and topological phases were analyzed. On this basis, edge states and corner states with topological protection properties were implemented, resulting in a relatively wider bandgap with a relative bandgap width of 35%. The unidirectional transmission characteristics and anti-interference ability of topological boundary states were verified through frequency domain simulation. Topological corner states can constrain light waves at corner positions. The results show that the photonic crystal structure based on the SSH model can achieve topological edge states and corner states with good performance. The structure is simple and easily realized.