Abstract: Curable polyolefin insulating material covering an electric cable core is continuously cured as it is drawn through a horizontal curing tube constituted of a number of units each composed of heating and cooling zones and a seal portion provided to separate one unit from another, the curing tube being filled with a high-viscosity heat transfer liquid. At each seal portion, the heat transfer liquid is super-cooled and increases its viscosity enough to seal the clearance between the outer surface of the insulated cable core and the inner wall surface of the curing tube to support the cable core with the least dip. This apparatus can improve production efficiency, and the finished product is free of any eccentricity or distortion of its shape.