Abstract: A porous ceramic filter has properties such that a porosity of the filter is more than 45% and less than 60%, a volume of pores having a pore size of less than 40 .mu.m is more than 60% of total volume of pores of the ceramic filter and an inequality of 1000M+85N.gtoreq.530 is satisfied, wherein M (m.sup.2 /g) is a specific surface of total pores continued from a surface to an inner portion of the filter and N (.mu.m) is a surface roughness of a surface of the filter. Preferably, the porous ceramic filter has a thermal expansion coefficient of less than 0.5.times.10.sup.-6 /.degree.C. within a temperature range of 40.degree..about.800.degree. C. in a direction parallel to a flow passage of the filter. The porous ceramic filter according to the invention is preferably used for eliminating soots in an exhaust gas from a diesel engine, and has a long operating time and requires less frequent filter regenerations.