A catalyst for olefin polymerization, comprising: a solid catalyst component comprising: a solid component on the surface of which hydroxyl groups are not detected by a method in which an excess amount of ethoxydiethylaluminum is reacted with the hydroxyl groups on the surface of the component to produce ethane gas, and the amount of the produced ethane gas is measured, and then the initial amount of hydroxyl groups on the surface of the component is obtained based on the amount of produced ethane gas, a compound of a transition metal selected from Groups 3-11 of the Periodic Table, and a mixture of an activator compound (C-1) capable of reacting with the transition metal compound to form a metal complex having catalytic activity and an organoaluminum compound (C-2); and an organomagnesium compound soluble in a hydrocarbon solvent which is obtained by reacting (i) an organomagnesium compound represented by the general formula: (Mt) α (Mg) β (R 1) a (R 2) b wherein Mt is a metal selected from Al, B, Be, Zn, Li, Na and K, R 1 and R 2 are hydrocarbon groups of 2-20 carbon atoms, and α, β, a and b are numerals satisfying the following relationship: 0<α, 0<β, 0≤a, 0≤b, a+b>0, and rα+2β=a+b (where r is a valence of Mt) with (ii) a compound selected from an amine compound, an alcohol compound and a siloxane compound. a solid catalyst component comprising: a solid component on the surface of which hydroxyl groups are not detected by a method in which an excess amount of ethoxydiethylaluminum is reacted with the hydroxyl groups on the surface of the component to produce ethane gas, and the amount of the produced ethane gas is measured, and then the initial amount of hydroxyl groups on the surface of the component is obtained based on the amount of produced ethane gas, a compound of a transition metal selected from Groups 3-11 of the Periodic Table, and a mixture of an activator compound (C-1) capable of reacting with the transition metal compound to form a metal complex having catalytic activity and an organoaluminum compound (C-2); and an organomagnesium compound soluble in a hydrocarbon solvent which is obtained by reacting (i) an organomagnesium compound represented by the general formula: (Mt) α (Mg) β (R 1) a (R 2) b wherein Mt is a metal selected from Al, B, Be, Zn, Li, Na and K, R 1 and R 2 are hydrocarbon groups of 2-20 carbon atoms, and α, β, a and b are numerals satisfying the following relationship: 0<α, 0<β, 0≤a, 0≤b, a+b>0, and rα+2β=a+b (where r is a valence of Mt) with (ii) a compound selected from an amine compound, an alcohol compound and a siloxane compound. a solid component on the surface of which hydroxyl groups are not detected by a method in which an excess amount of ethoxydiethylaluminum is reacted with the hydroxyl groups on the surface of the component to produce ethane gas, and the amount of the produced ethane gas is measured, and then the initial amount of hydroxyl groups on the surface of the component is obtained based on the amount of produced ethane gas, a compound of a transition metal selected from Groups 3-11 of the Periodic Table, and a mixture of an activator compound (C-1) capable of reacting with the transition metal compound to form a metal complex having catalytic activity and an organoaluminum compound (C-2); and an organomagnesium compound soluble in a hydrocarbon solvent which is obtained by reacting (i) an organomagnesium compound represented by the general formula: (Mt) α (Mg) β (R 1) a (R 2) b wherein Mt is a metal selected from Al, B, Be, Zn, Li, Na and K, R 1 and R 2 are hydrocarbon groups of 2-20 carbon atoms, and α, β, a and b are numerals satisfying the following relationship: 0<α, 0<β, 0≤a, 0≤b, a+b>0, and rα+2β=a+b (where r is a valence of Mt) with (ii) a compound selected from an amine compound, an alcohol compound and a siloxane compound.