A catalyst converter having a retaining mat with a thickness wherein the apparent density during assembling becomes 0.25 g/cm3 or more and less than 0.51 g/cm3 and the outside diameter D1 of a catalyst retainer is set according to interference of the retaining mat in passing through a press-in tool and interference of the retaining mat after being pressed into a retaining tube. The retaining mat is formed of a non-expandable inorganic fiber sheet. A pressing force moves the catalyst retainer in the axial direction with respect to the retaining tube while the catalyst converter device is used with the length L2 along the longitudinal direction of the catalyst retainer in the retaining mat wound around the catalyst retainer being set longer than the winding diameter D1 of the retaining mat around the catalyst retainer so that a retaining force R greater than the pressing force F can be secured.