An inert hydrocarbon solvent-soluble catalyst for polymerization of olefinic hydrocarbons and a process for producing an olefinic polymer using the same are disclosed, the catalyst being composed of (A) a reaction product obtained by reacting (a) at least one vanadium compound represented by formula:VO(OR).sub.m X.sub.3-mwherein R represents a hydrocarbon group; X represents a halogen atom; and m represents a real number of from 0 to 3, and (b) a dihydroxy hydrocarbon compound constituted of a straight chain hydrocarbon skeleton containing from 2 to 12 carbon atoms and having a hydroxyl group at each of both terminals thereof and at least one hydrocarbon branch bonded to said hydrocarbon skeleton in an inert hydrocarbon solvent at an (a) to (b) molar ratio of from 1:0.5 to 1:1.4 and (B) at least one organoaluminum compound represented by formula:R'.sub.n AlX'.sub.3-nwherein R' represents a hydrocarbon group X' represents a halogen atom; and n represents a real number more than 0 and less than 3. Olefinic hydrocarbon polymers having narrow distributions of molecular weight and composition can be produced with high efficiency and high polymerization activity without being accompanied by obstruction or contamination of equipment due to precipitation of a catalyst.