The relationship between the topological phase of matter and interactions of the system was confirmed for the Kekulé lattice. The impact of non-Hermitian effect on topological insulator was investigated. Two types of gain and loss configurations were designed to illustrate their effects on bulk energy spectra and edge energy spectra. It is found that the bandgap decreases with the increase of the gain and loss, and is eventually closed and forms a non-Hermiticity-induced Dirac point. Finally, the Dirac point splits into a pair of singular points. Distinguishing from traditional Kekulé lattice, intercellular coupling is differentiated into horizontal and vertical dimensions for independent control based on the same intracellular coupling. This approach verifies that the gapless edge mode is not only related to geometric boundary, but also regulated by the intercellular coupling of the system.