The invention relates to a process for preparing a poly-1-olefin by polymerization of a 1-olefin of the formula R4CH═CH2, where R4 is hydrogen or an alkyl radical having from 1 to 10 carbon atoms, in suspension, in solution or in the gas phase, at a temperature of from 20 to 200° C. and a pressure of from 0.5 to 50 bar, in the presence of a catalyst which comprises the reaction product of a magnesium alkoxide with a transition metal compound (=component a) and an organometallic compound (=component b) and whose component a has been prepared in a manner having the feature that a magnesium alkoxide powder having a mean particle size, expressed as the d50, in the range from 100 to 1000 μm is firstly processed by dry milling in a mill under inert conditions to produce magnesium alkoxide powder having a mean particle size, expressed as the d50, of less than 15 μm, then suspended in an inert hydrocarbon in which the magnesium alkoxide is insoluble, and is reacted immediately without further pretreatment with a transition metal compound of titanium, zirconium, vanadium or chromium.