Disclosed are an apparatus and a method for manufacturing a heat insulator, including: a frame having a feeder provided at front side of the frame for feeding a cross-linked foam polyethylene sheet and a winder provided at rear side of the frame for winding a completed heat insulator; a cutting part provided at a leading side of the frame, a widening part provided at a rear side of the cutting part, which is for transforming the cutoff slots into cells by widening a width of the cross-linked foam polyethylene sheet formed with the cutoff slots; a cooling part provided at a rear side of the widening part, which has cooling rollers to continuously maintain a widened width of the cross-linked foam polyethylene sheet and a shape of the cells transformed from the cutoff slots; and a sheet-attaching part provided at a rear side of the cooling part.