In non-line-of-sight imaging scenes, while effective echo photons are reduced to a great extent, Poisson noise largely impacts the non-line-of-sight imaging quality. Moreover, issues such as long iteration time, fixed mode, and manual parameter setting have been identified with traditional image Poisson noise suppression algorithms. Therefore, to improve the quality of non-line-of-sight imaging, this study designed a deep learning-based Poisson noise suppression method for single-photon non-line-of-sight imaging. First, geometrical optics approximation and Monte Carlo methods were implemented to track and model the photon motion trajectory in the non-line-of-sight scene, simulate the non-line-of-sight imaging process, produce a dataset using the Poisson noise images reconstructed from the simulation data, and address the problem of insufficient training samples. Subsequently, we designed an attention-based feature-enhanced noise suppression network (AEF-Net), followed by optimization and training of the network using simulation data. Furthermore, we built a non-line-of-sight imaging system to verify the Poisson noise suppression performance of the network. The experimental results show an outperformance of our designed noise suppression attention-based feature-enhanced noise suppression network than the conventional noise suppression algorithms for removing Poisson noise from non-line-of-sight scenes.