Deep learning networks have been applied to under-sampled single-pixel imaging (SPI) for better reconstruction performance. However, the existing deep-learning-based SPI methods with convolutional filters have difficulty in modeling long-range dependencies of SPI measurements and thus show limited reconstruction quality. Recently, the transformer has demonstrated great potential in capturing long-range dependencies, but it lacks locality mechanism and thus could be sub-optimal when directly used for under-sampled SPI. In this Letter, we propose a high-quality under-sampled SPI method based on a novel, to the best of our knowledge, local-enhanced transformer. The proposed local-enhanced transformer is not only good at capturing global dependencies of SPI measurements, but also has the capability to model local dependencies. Additionally, the proposed method employs optimal binary patterns, which makes the sampling high-efficiency and hardware-friendly. Experiments on simulated data and real measured data demonstrate that our proposed method outperforms the state-of-the-art SPI methods.