In an X-ray detector and method for applying a stray radiation grid onto an X-ray detector having detector elements arranged in a matrix that form a detector surface having detection regions sensitive to X-rays and less sensitive intermediate regions, a basic structure for the stray radiation grid is built up over the detector surface directly on the X-ray detector with a rapid prototyping technique and is subsequently coated or filled with a material that is highly absorbent for X-radiation. An absorbent structure thus arises that lies over the less sensitive intermediate regions of the detector surface. Moiré disturbances are avoided in the X-ray image exposure and the detective quantum efficiency (DQE) is increased.