A semiconductor package includes a substrate having thereon at least an antenna layer and a ground reflector layer under the antenna layer, a radio frequency (RF) die disposed on or in the substrate, an encapsulation layer disposed on the antenna layer of the substrate, and a frequency-selective surface (FSS) structure disposed on the encapsulation layer. The FSS structure is a two-dimensional periodic array of metal patterns of same shape and size. The FSS structure has highly reflective characteristic.