A ceramic catalyst carrier has a honeycombed structure which comprises a plurality of elongated parallel preferably square channels and thin, porous walls. The thickness of the walls is between 0.4 mm and 1.2 mm. The open cross-sectional area of the channels is greater than 80% of the total cross-section of the carrier body. Besides an intended low primary porosity, a secondary porosity is produced by an opening material. The pores of the secondary porosity which enlarge the active surface for the catalyst show a selected pore size distribution curve with negative skewness and a modal value ranging from 4,000 nm to 60,000 nm. The total true porosity amounts preferably between 50 and 70 Vol. % of the ceramic, whereby the ratio between total and secondary porosity is in the range of 1:1 to 6:1. By ceramic fibres the mechanical strength of the thin walls of the soft green clot and of the fired porous structure can be improved. According to the process the compounds are mixed to achieve a certain plasticity, aged and extruded to form a honeycombed structure which is thereupon dried and fired.