To provide a polyolefin polymer having a polar group represented by Formula (i) produced by modifying, with a high modification ratio, a double bond in a polymer having the double bond at one terminal, both terminals, or at the inside of a polymer chain thereof that is obtained by a known method; a method for producing the polyolefin polymer; and a water dispersion material and a mold release agent composition each containing the polyolefin polymer, ##STR00001## wherein in Formula (i), PO represents a polyolefin polymer obtained by polymerizing a monomer including ethylene or including an olefin having 3 to 20 carbon atoms, and a group shown in the brackets is the polar group of the polyolefin polymer; A and B each independently represent R.sup.1, a cyano group, C(O)OR.sup.1, or C(O)NR.sup.1R.sup.2, and A and B may be combined to form a cyclic structure; M represents a metal cation or an onium cation; j is an integer of 0 to 4 representing the number of the metal cation or the onium cation; i is an integer of 0 to 4 representing the number of valency of the metal cation or the onium cation; D and E each independently represent an oxygen atom, a nitrogen atom, a sulfur atom, R.sup.3, OR.sup.3, SR.sup.3, or NR.sup.3R.sup.4, and D and E may be combined to form a cyclic structure; d and e each independently are an integer of 0 to 4 representing respectively the number of valency of the substituent D and the number of valency of the substituent E; R.sup.1, R.sup.2, R.sup.3, and R.sup.4 each independently represent hydrogen, an optionally substituted alkyl, alkenyl, alkynyl, aralkyl or aryl group having 20 or less carbon atoms, or a group having a heterocyclic ring; and n represents the average number of functional groups, and ranges from 0.80 to 10.0.