Molecular property prediction is a fundamental task of drug discovery. With the rapid development of deep learning, computational approaches for predicting molecular properties are experiencing increasing popularity. However, these existing methods often ignore the 3D information on molecules, which is critical in molecular representation learning. In the past few years, several self-supervised learning (SSL) approaches have been proposed to exploit the geometric information by using pre-training on 3D molecular graphs and fine-tuning on 2D molecular graphs. Most of these approaches are based on the global geometry of molecules, and there is still a challenge in capturing the local structure and local interpretability. To this end, we propose local geometry-guided graph attention (LGGA), which integrates local geometry into the attention mechanism and message-passing of graph neural networks (GNNs). LGGA introduces a novel method to model molecules, enhancing the model's ability to capture intricate local structural details. Experiments on various data sets demonstrate that the integration of local geometry has a significant impact on the improved results, and our model outperforms the state-of-the-art methods for molecular property prediction, establishing its potential as a promising tool in drug discovery and related fields.