Recent advances in autonomous driving have greatly increased the focus on place recognition technology, a crucial aspect of environmental perception. However, current multimodal fusion techniques for combining camera and LiDAR data often neglect the distinct measurement attributes of these sensors, thereby restricting the efficiency of accurate place identification. In this work, we introduce LoG-PR, a multimodal place recognition approach that integrates 2D local and 3D global features and combines them through cross-attention to improve recognition accuracy. Our approach handles each modality separately, generating a comprehensive descriptor tensor through data fusion and key point enhancement, leveraging the unique strengths of both sensors. We simultaneously employ voxel-based and point-based methods for capturing global characteristics of the surveyed environmental point cloud, while utilizing residual neural networks to extract intricate local features from images. To effectively exploit the potential correlations between images and point clouds, we develop a cross-attention transformer that integrates complementary information from diverse modalities while preserving the original feature information. We test our method on the open-source benchmarks including Oxford RobotCar, NCLT, KITTI and MUN-FRL. The results demonstrate a significant performance improvement compared to existing SOTA methods, effectively enhancing the accuracy and robustness of place recognition. Our code is publicly accessible at: https://github.com/LuXu01/Log-PR .