The present invention relates to a method of homo- or co-
polymerization of alpha-olefin by means of using a catalyst 
system which comprises the following components: (1) a 
solid complex 
titanium catalyst produced by means of a production method comprising the following steps: (a) preparing a 
magnesium compound solution by dissolving a 
magnesium halide compound and a compound of Group IIIA of the Periodical Table in a 
solvent of mixture of cyclic ester, one or more types of 
alcohol, a 
phosphorus compound, and an organic 
silane; (b) precipitating the 
solid particles by reacting said 
magnesium compound solution with a transitional 
metal compound, a 
silicon compound, a 
tin compound, or the mixture thereof; and (c) reacting said precipitated 
solid particles with a 
titanium compound and 
electron donors; (2) an organometallic compound of 
metal of Group IIIA of the Periodical Table; and (3) external 
electron donors comprising three or more types of organo-
silicon compounds, wherein the melt flow rates of the homopolymers obtained from 
polymerization by individually using said organo-
silicon compounds under the same 
polymerization conditions are 5 or less, 5~20, and 20 or higher, respectively. According to the present invention, it has an 
advantage of obtaining polymers of broad molecular 
weight distribution with high 
hydrogen reactivity and melt flow rates while maintaining high stereoregularity and yields for olefin homo- or co-polymers during homo- or co-polymerization of alpha-olefin having three or more carbon atoms.