An integrated circuit package includes a die mounted on a substrate, an integrated heat spreader set above the die, and an array of carbon nanotubes mounted between the die and the integrated heat spreader. The integrated heat spreader is fixed on the substrate, and includes an inner face. The array of carbon nanotubes is formed on the inner face of the integrated heat spreader. Top and bottom ends of the carbon nanotubes perpendicularly contact the integrated heat spreader and the die respectively. Each carbon nanotube can be capsulated in a nanometer-scale metal having a high heat conduction coefficient.