A ceramic honeycomb structure having a large number of flow paths partitioned by porous cell walls, the cell walls comprising at least main crystals of aluminum titanate, in which MgO and SiO2 are dissolved to form a solid solution, and glass phases, the glass phases containing 40-80% by mass of SiO2 and 1-20% by mass of MgO, the average size of the glass phases being 30 μm or less in a cross section of the cell walls, and the area ratio of the glass phases to the total area of the main crystals of aluminum titanate and the glass phases being 2-12% in a cross section of the cell walls, and its production method.