Photonic spin Hall effect (PSHE) of the transmitted wave presents promising applications in photonic spintronic devices, including inter-chip optical circuitry and quantum computing devices. These applications can benefit from phenomena such as the photon tunneling effect, frustrated total internal reflection, and the resonant optical tunneling effect. However, the mechanisms for enhancing PSHE of the transmitted wave are limited. In this study, an alternative strategy is proposed, which involves the utilization of topological edge states to enhance PSHE without relying on the aforementioned means. To demonstrate this effect, a heterostructure is designed, comprising two one-dimensional photonic crystals (PhCs) and a monolayer graphene. By leveraging the topological edge state, a significant enhancement of PSHE in the transmitted wave is observed, surpassing several times the incident wavelength. Furthermore, it is shown that the enhanced PSHE can be controlled and fine-tuned by adjusting the Fermi energy of monolayer graphene and the repetition numbers of the two PhCs. The enhanced and controlled PSHE in this heterostructure introduces possibilities for the development of novel optical components, such as switches, filters, modulators, and sensors.