Previous studies on phase contrast imaging (PCI) mammography have demonstrated an enhancement of breast morphology and cancerous tissue visualization compared to conventional imaging. We show here the first results of the PCI analyser-based imaging (ABI) in computed tomography (CT) mode on whole and large (>12 cm) tumour-bearing breast tissues. We demonstrate in this work the capability of the technique of working at high x-ray energies and producing high-contrast images of large and complex specimens. One entire breast of an 80-year-old woman with invasive ductal cancer was imaged using ABI-CT with monochromatic 70 keV x-rays and an area detector of 92×92 µm² pixel size. Sagittal slices were reconstructed from the acquired data, and compared to corresponding histological sections. Comparison with conventional absorption-based CT was also performed. Five blinded radiologists quantitatively evaluated the visual aspects of the ABI-CT images with respect to sharpness, soft tissue contrast, tissue boundaries and the discrimination of different structures/tissues. ABI-CT excellently depicted the entire 3D architecture of the breast volume by providing high-resolution and high-contrast images of the normal and cancerous breast tissues. These results are an important step in the evolution of PCI-CT towards its clinical implementation.