The present invention relates to a magnesium compound-supported nonmetallocene catalyst, which is produced by directly contacting a catalytically active metallic compound with a nonmetallocene ligand-containing magnesium compound, or by directly contacting a nonmetallocene ligand with a catalytically active metal-containing magnesium compound, through an in-situ supporting process. The process is simple and flexible. In the process, there are many variables in response for adjusting the polymerization activity of the catalyst, and the margin for adjusting the catalyst load or the catalyst polymerization activity is broad. The magnesium compound-supported nonmetallocene catalyst according to this invention can be used for olefin homopolymerization/copolymerization, in combination with a comparatively less amount of the co-catalyst, to achieve a comparatively high polymerization activity. Further, the polymer product obtained therewith boasts high bulk density and adjustable molecular weight distribution.