We demonstrate computational ghost imaging at X-ray wavelengths with only one single-pixel detector. We show that, by using a known designed mask as a diffuser that induces intensity fluctuations in the probe beam, it is possible to compute the propagation of the electromagnetic field in the absence of the investigated object. We correlate these calculations with the measured data when the object is present in order to reconstruct the images of 50 μm and 80 μm slits. Our results open the possibilities for X-ray high-resolution imaging with partially coherent X-ray sources and can lead to a powerful tool for X-ray three-dimensional imaging.