Advances in x-ray imaging have enabled breakthroughs in medicine, biology, materials science, and cultural heritage studies. Three-dimensional visualizations of micrometer-scale structures inside soft tissues and dense specimens have been made successful by state-of-the-art methods based on hard x-ray phase-contrast imaging. Nevertheless, it remains challenging to achieve high spatial resolutions without increasing radiation dose and risking damage to specimens. A promising approach to reduce dose and still achieve high spatial resolution is x-ray ghost imaging, which uses singlepixel, yet efficient direct x-ray detectors made of high-density materials. However, all currently existing x-ray ghost imaging protocols are unable to achieve phase contrast and suffer from low-quality image reconstructions. Here, we present an efficient approach which exploits structured-detection single-pixel imaging in order to produce an x-ray ghost image with phase contrast, accuracy, and high fidelity. The resulting x-ray phase-contrast ghost images provide accurate information regarding density variations in the sample and visibly render edges that are otherwise invisible with x-ray attenuation contrast. This demonstration of phase-contrast ghost imaging with x-rays has the potential to promote x-ray ghost imaging from a niche technique to a routinely applied method.