A catalyst which efficiently removes particulate matter, SOF, sulfate, and SOOT and the like from the exhaust gas from such an internal combustion engine as a diesel engine without inducing a rise in the back pressure of the engine is provided. The catalyst for the purification of the exhaust gas of an internal combustion engine is formed by using an open flow honeycomb containing in the channel walls thereof such pores as possess an average diameter in the range of 10-40 .mu.m.