A heat dissipating structure and a semiconductor package with the same are proposed. A substrate is used to accommodate at least one chip thereon, and the chip is electrically connected to the substrate. A heat dissipating structure having a flat portion and a support portion is mount on the substrate via the support portion by means of an adhesive. At least one groove is formed on the support portion and at least one air vent is formed around the groove to allow the groove to communicate with the outside via the air vent, such that the adhesive is allowed to fill the groove to expel air from the groove to the atmosphere through the air vent, thereby preventing the air from trapped in the groove.