A catalyst component for the polymerization of olefins comprises Mg, Ti, halogen, and an alpha-omega-diether represented by the general formula: (RO)—(CR1R2)n—(OR), wherein the number of n is from 5 to 10, R is an alkyl, cycloalkyl or aryl radical containing 1 to 12 carbons, and R1 and R2 are independently from each other hydrogen, an alkyl, cycloalkyl or aryl radical containing 1 to 12 carbons. The catalysts prepared with such component provide a high mileage for the production of polyolefins with a high bulk density of the polymer produced in gas-phase polymerization process or in slurry polymerization process. Such catalyst produces narrower MWD PE, if compared with other catalyst systems.