Highly crystalline higher alpha-olefin polymer and process for production thereof

A highly crystalline higher alpha-olefin polymer that is excellent in compatibility with a thermoplastic resin, particularly a polyolefin, compatibility with a lubricant oil, a fuel oil and wax, mixing property with an inorganic filler, and secondary working property, and a process for production thereof are provided. The highly crystalline higher alpha-olefin polymer is obtained by polymerizing a monomer containing 80% by mol or more of a higher alpha-olefin having from 22 to 40 carbon atoms, and satisfies the following items (1) and (2). (1) The melting point (Tm), which is observed, by using a differential scanning calorimeter (DSC), from a melting endothermic curve obtained by maintaining a specimen at 190° C. for 5 minutes under a nitrogen atmosphere, cooling the specimen to -10° C. at a rate of 5° C./min, maintaining at -10° C. for 5 minutes, and then elevating a temperature thereof to 190° C. at a rate of 10° C./min, is from 55 to 100° C. (2) Standards weight average molecular weight (Mw) measured by a gel permeation chromatography (GPC) based on polystyrene is from 1,000 to 5,000,000, and the molecular weight distribution (Mw/Mn) measured thereby is 5.0 or less.