A heater includes: a conductive ceramic cylinder tube provided with a plurality of cells, each cell being defined by a pair of first cell-walls and a pair of second cell-walls, each first cell-wall extending in a radial direction of the ceramic cylinder tube, and each second cell-wall extending so as to cross the radial direction of the ceramic cylinder tube; an inner electrode electrically coupled to an inner wall of the ceramic cylinder tube; and an outer electrode electrically coupled to an outer wall of the ceramic cylinder tube. Linear portions are radially arranged in the ceramic cylinder tube, each linear portion linearly extending in the radial direction of the ceramic cylinder tube so as to include a plurality of first cell-walls that are arranged on the same axial line that in the radial direction and current flows radially at least via the linear portions between the inner and outer electrodes.