Preterm infants (born between 28 and 37 weeks of gestation) face elevated risks of neurodevelopmental delays, making early identification crucial for timely intervention. While deep learning-based volumetric segmentation of brain MRI scans offers a promising avenue for assessing neonatal neurodevelopment, achieving accurate segmentation of white matter (WM) and gray matter (GM) in preterm infants remains challenging due to their comparable signal intensities (isointense appearance) on MRI during early brain development. To address this, we propose a novel segmentation neural network, named Hierarchical Dense Attention Network. Our architecture incorporates a 3D spatial-channel attention mechanism combined with an attention-guided dense upsampling strategy to enhance feature discrimination in low-contrast volumetric data. Quantitative experiments demonstrate that our method achieves superior segmentation performance compared to state-of-the-art baselines, effectively tackling the challenge of isointense tissue differentiation. Furthermore, application of our algorithm confirms that WM and GM volumes in preterm infants are significantly lower than those in term infants, providing additional imaging evidence of the neurodevelopmental delays associated with preterm birth. The code is available at: https://github.com/ICL-SUST/HDAN.