Human brain tissue belongs to the most impressive and delicate three-dimensional structures in nature. Its outstanding functional importance in the organism implies a strong need for brain imaging modalities. Although magnetic resonance imaging provides deep insights, its spatial resolution is insufficient to study the structure on the level of individual cells. Therefore, our knowledge of brain microstructure currently relies on two-dimensional techniques, optical and electron microscopy, which generally require severe preparation procedures including sectioning and staining. X-ray absorption microtomography yields the necessary spatial resolution, but since the composition of the different types of brain tissue is similar, the images show only marginal contrast. An alternative to absorption could be X-ray phase contrast, which is known for much better discrimination of soft tissues but requires more intricate machinery. In the present communication, we report an evaluation of the recently developed X-ray grating interferometry technique, applied to obtain phase-contrast as well as absorption-contrast synchrotron radiation-based microtomography of human cerebellum. The results are quantitatively compared with synchrotron radiation-based microtomography in optimized absorption-contrast mode. It is demonstrated that grating interferometry allows identifying besides the blood vessels, the stratum moleculare, the stratum granulosum and the white matter. Along the periphery of the stratum granulosum, we have detected microstructures about 40 µm in diameter, which we associate with the Purkinje cells because of their location, size, shape and density. The detection of individual Purkinje cells without the application of any stain or contrast agent is unique in the field of computed tomography and sets new standards in non-destructive three-dimensional imaging.