The invention relates to a modified Ziegler catalyst for preparing a poly-1-olefin in suspension, in solution or in the gas phase, which catalyst comprises the reaction product of a magnesium alkoxide (component a) with a transition metal compound (component b) and an organometallic compound (component c) together with an additional component (d) comprising a compound of the chemical formula M—Rx where M is an element of main group IV of the Periodic Table, R is halogen or an organic radical such as alkyl having from 1 to 10 carbon atoms, oxyalkyl having from 1 to 10 carbon atoms, cycloalkyl having from 4 to 8 carbon atoms in the ring and, if desired, from 1 to 6 substituents R′ on the ring, aryl having from 6 to 10 carbon atoms in the aromatic and, if desired, from 1 to 6 substituents R′ on the aromatic, where R′ is a halogen or an alkyl radical having from 1 to 4 carbon atoms or an OH group or an NO2 group or an oxyalkyl radical having from 1 to 4 carbon atoms, and x is an integer from 1 to 4. The invention also relates to a process for preparing the Ziegler catalyst and to the homopolymerization or copolymerization of 1-olefins in its presence.