The ceramics honeycomb structure of the present invention is formed of a plurality of cells forming a fluid flow passage partitioned by porous partition walls, and comprising an inflow end part allowing fluid to flow therein, an outflow end part allowing fluid to flow therefrom, and an outer peripheral part including an outer peripheral surface, and is characterized by having a structure where a porosity per unit volume (cm.sup.3) gradually increases from the inflow end part side to the outflow end part side at a rate of 0.2%/mm or less, and this ceramics honeycomb structure has an excellent erosion resistance of partition walls positioned at a cell opening end part and a high compressive strength (isostatic strength) at the time of canning, and is suitable particularly as an automobile exhaust gas purification catalyst carrier.