To achieve immersive spatial audio rendering on VR/AR devices, high-quality Head-Related Transfer Functions (HRTFs) are essential. In general, HRTFs are subject-dependent and position-dependent, and their measurement is time-consuming and tedious. To address this challenge, we propose the Graph Neural Field with Spatial-Correlation Augmentation (GraphNF-SCA) for HRTF personalization, which can be used to generate individual HRTFs for unseen subjects. The GraphNF-SCA consists of three key components: an HRTF personalization (HRTF-P) module, an HRTF upsampling (HRTF-U) module, and a fine-tuning stage. In the HRTF-P module, we predict HRTFs of the target subject via the Graph Neural Network (GNN) with an encoder-decoder architecture, where the encoder extracts universal features and the decoder incorporates the target-relevant features and produces individualized HRTFs. The HRTF-U module employs another GNN to model spatial correlations across HRTFs. This module is fine-tuned using the output of the HRTF-P module, thereby enhancing the spatial consistency of the predicted HRTFs. Unlike existing methods that estimate individual HRTFs position-by-position without spatial correlation modeling, the GraphNF-SCA effectively leverages inherent spatial correlations across HRTFs to enhance the performance of HRTF personalization. Experimental results demonstrate that the GraphNF-SCA achieves state-of-the-art results.