To obtain a composite metal cyanide complex catalyst that shortens an induction period until the initiation of a reaction without increasing the loading of the catalyst in ring opening polymerizing an alkylene oxide using the composite metal cyanide complex catalyst.

The composite metal cyanide complex catalyst, of which the number of cyanoferrate (III) ion is from 0.02 to 0.95 when the total number of cyanocobaltate ion and cyanoferrate (III) ion is 1, is manufactured by reacting a transition metal cyanide compound wherein the transition metal is cobalt, a transition metal cyanide compound wherein the transition metal is tervalent iron and a metal halide salt with an organic ligand in an aqueous medium.