Contactless palmprint recognition has gained traction due to its convenience and hygienic benefits. However, in real-world scenarios with complex backgrounds and varying hand poses, evaluating image quality to enhance recognition performance remains a significant challenge. To address this, we propose a novel Hand-Geometry Aware Contactless Palmprint Image Quality Assessment (HGAIQA) framework. Unlike existing methods that assess only the palmprint ROI, our framework evaluates the entire image. Firstly, it employs a high-resolution hand segmentation network and keypoint heatmap module to identify hand region and joint keypoints. Secondly, it evaluates the palm's flatness based on geometric features and assesses additional quality attributes such as brightness and sharpness. Lastly, it determines image quality by analyzing the intra-class and inter-class distributions of fused multi-features. After integrating with subsequent ROI localization and recognition algorithms, experiments show a substantial 21.2% reduction in EER for palmprint recognition on the COEP database by removing the lowest 10% of low-quality images. These results demonstrate the effectiveness of our approach in significantly enhancing palmprint recognition performance.