The invention relates to a process for preparing a catalyst for the polymerization of olefins, which comprises: a) preparation of a finely divided silica xerogel, b) loading of the xerogel with chromium from a solution of chromium trioxide or a chromium compound which is converted into chromium trioxide under the conditions of step c), and c) activation of the resulting product at from 400 to 1100.degree. C. in a water-free gas stream comprising oxygen in a concentration of above 10% by volume, wherein a fluoride doping with a fluorinating agent is carried out in step b) or in step c). Furthermore, the invention relates to a catalyst for the polymerization of olefins which is obtainable by the process of the invention and to a process for the polymerization of olefins in which an olefin or an olefin mixture is polymerized in the presence of a catalyst according to the invention.