To provide a solid double metal cyanide catalyst capable of improving the activity of an epoxide polymer by reacting an aq. metal salt soln. with an aq. metal cyanide salt soln. and mixing the resultant catalyst slurry with a specific polyether.

An aq. soln. contg. an excess metal salt is reacted with an aq. soln. of a metal cyanide salt in the presence of an org. complexing agent to give a catalyst slurry. The slurry is mixed with 5-80 wt.% polyether having a number average mol.wt. of 500 or higher and an average hydroxyl functionality of 2-8, and the resultant polyether-contg. solid catalyst is separated from the slurry. Then, the solid catalyst is washed with an aq. soln. contg. an org. complexing agent to give a solid double metal cyanide catalyst contg. a divalent cyanide compd., an org. complexing agent, and a polyether.