Polyolefin polymer containing vinyl groups at both ends and composition thereof

A polyolefin polymer containing vinyl groups at both ends thereof, containing a constitutional unit derived from at least one selected from the group consisting of an α-olefin having 3 to 20 carbon atoms (b), and a cyclic olefin (c) represented by the following general formula[III];

• obtained by metathesis reaction;
• and having
• (1) a ratio of terminal vinylation of 70% or more relative to all of both ends of molecular chains, and
• (2) an intrinsic viscosity [η] in the range of 0.01 to 10 dl/g as measured in a decahydronaphthalene solution at 135° C.,
• the α-olefin (b) being a propylene (e) and at least one kind of an α-olefin (f) having 4 to 20 carbon atoms,
• the constitutional unit derived from the propylene (e) satisfying any one of the following conditions i) to iii)
• i) a mesotriad fraction (mm) obtained from 13C-NMR is 50% or more;
• ii) a racemotriad fraction (rr) obtained from 13C-NMR is 50% or more;
• iii) a mesotriad fraction obtained from 13C-NMR is less than 50% and a racemotriad fraction obtained from 13C-NMR is less than 50%:
• wherein each of R100 and R101 may be the same or different and represents a hydrogen atom or a hydrocarbon group having 1 to 5 carbon atoms;
• and f represents an integer of 1≦f≦18.