A process for producing a magnesium compound-supported nonmetallocene catalyst, which comprises: a contacting step of contacting a magnesium compound with one of the two: i) a chemical treating agent and ii) a nonmetallocene ligand, in a solvent which does not dissolve the magnesium compound, upon finish of the reaction i), the resultant mixture is subjected to filtration, washing and drying, or upon finish of the reaction ii) the resultant mixture is subjected to filtration and washing or to filtration, washing and drying, to obtain a contact resultant, wherein the chemical treating agent is a Group IVB metal compound; and a treating step of treating the contact resultant with the other of the two: the chemical treating agent and the nonmetallocene ligand, so as to obtain the magnesium compound-supported nonmetallocene catalyst, wherein the nonmetallocene ligand is a compound having the following structure, wherein: q is 0 or 1; d is 0 or 1; A is selected from the group consisting of an oxygen atom, a sulfur atom, a selenium atom, -NR 23 R 24, -N R 25 R 26, -PR 28 R 29, -P R 30 OR 31, a sulfone group, a sulfoxide group and -Se R 39; B is selected from the group consisting of a nitrogen-containing group, a phosphor-containing group, and a C 1 -C 30 hydrocarbyl; D is selected from the group consisting of an oxygen atom, a sulfur atom, a selenium atom, a nitrogen-containing C 1 -C 30 hydrocarbyl, a phosphor-containing C 1 -C 30 hydrocarbyl, a sulfone group, a sulfoxide group, -N R 25 R 26, and -P R 32 (OR 33), wherein N, O, S, Se and P each represent a coordination atom; E is selected from the group consisting of a nitrogen-containing group, an oxygen-containing group, a sulfur-containing group, a selenium-containing group and a phosphor-containing group, wherein N, O, S, Se and P each represent a coordination atom; G is selected from the group consisting of a C 1 -C 30 hydrocarbyl, a substituted C 1 -C 30 -hydrocarbyl and an inert functional group; → represents a single bond or a double bond; - represents a covalent bond or an ionic bond; and R 1 to R 3, R 22 to R 33, and R 39 are each independently selected from the group consisting of hydrogen, a C 1 -C 30 hydrocarbyl, a halogen atom, a substituted C 1 -C 30 hydrocarbyl and an inert functional group, wherein these groups can be identical to or different with each other, and any adjacent groups can optionally form a bond or a ring altogether. a contacting step of contacting a magnesium compound with one of the two: i) a chemical treating agent and ii) a nonmetallocene ligand, in a solvent which does not dissolve the magnesium compound, upon finish of the reaction i), the resultant mixture is subjected to filtration, washing and drying, or upon finish of the reaction ii) the resultant mixture is subjected to filtration and washing or to filtration, washing and drying, to obtain a contact resultant, wherein the chemical treating agent is a Group IVB metal compound; and i) a chemical treating agent and ii) a nonmetallocene ligand, a treating step of treating the contact resultant with the other of the two: the chemical treating agent and the nonmetallocene ligand, so as to obtain the magnesium compound-supported nonmetallocene catalyst, q is 0 or 1; d is 0 or 1; A is selected from the group consisting of an oxygen atom, a sulfur atom, a selenium atom, -NR 23 R 24, -N R 25 R 26, -PR 28 R 29, -P R 30 OR 31, a sulfone group, a sulfoxide group and -Se R 39; B is selected from the group consisting of a nitrogen-containing group, a phosphor-containing group, and a C 1 -C 30 hydrocarbyl; D is selected from the group consisting of an oxygen atom, a sulfur atom, a selenium atom, a nitrogen-containing C 1 -C 30 hydrocarbyl, a phosphor-containing C 1 -C 30 hydrocarbyl, a sulfone group, a sulfoxide group, -N R 25 R 26, and -P R 32 (OR 33), wherein N, O, S, Se and P each represent a coordination atom; E is selected from the group consisting of a nitrogen-containing group, an oxygen-containing group, a sulfur-containing group, a selenium-containing group and a phosphor-containing group, wherein N, O, S, Se and P each represent a coordination atom; G is selected from the group consisting of a C 1 -C 30 hydrocarbyl, a substituted C 1 -C 30 -hydrocarbyl and an inert functional group; → represents a single bond or a double bond; - represents a covalent bond or an ionic bond; and → represents a single bond or a double bond; - represents a covalent bond or an ionic bond; and R 1 to R 3, R 22 to R 33, and R 39 are each independently selected from the group consisting of hydrogen, a C 1 -C 30 hydrocarbyl, a halogen atom, a substituted C 1 -C 30 hydrocarbyl and an inert functional group, wherein these groups can be identical to or different with each other, and any adjacent groups can optionally form a bond or a ring altogether.