A semiconductor die package and a method of forming the same are provided. The semiconductor die package includes a package substrate, and a first semiconductor die and a second semiconductor die disposed thereon. A ring structure is attached to the package substrate and surrounds the semiconductor dies. A lid structure is attached to the ring structure and disposed over the semiconductor dies, and has an opening exposing the second semiconductor die. A heat sink is disposed over the lid structure and has a portion extending into the opening of the lid structure. A first thermal interface material (TIM) layer is interposed between the lid structure and the first semiconductor die. A second TIM layer is interposed between the extending portion of the heat sink and the second semiconductor die. The first TIM layer has a thermal conductivity higher than the thermal conductivity of the second TIM layer.