A heat-dissipation apparatus of the portable computer is fabricated in a host and a display unit pivotal connected therein for dissipating the heat from the electronic component. The apparatus has a conductive part whose thickness is designed to be equal to the thickness of the portable computer when closed. The conductive part has a first connecting portion and a second connecting portion, which the second connecting portion is used to be inserted by a cooling end of a first heat pipe. The heating end of the first heat pipe extends into the host and faces to the electronic component. The first connecting portion is used to be inserted by a heating end of a second heat pipe. The cooling end of the second heat pipe extends to the display unit.