A semiconductor package has a substrate made of WCu, WAg, MoCu or MoAg. A plurality of leads are fixed to the substrate by hermetic sealing without an intervening nickel plating layer. A cover is bonded to the substrate with a seal ring which is directly bonded to the substrate by brazing without an intervening nickel plating layer. The leads are nickel plated and gold plated after hermetic sealing, and the seal ring is nickel plated and gold plated after brazing. Even though the substrate is made of a metal alloy, this arrangement provides the package with a high degree of air tightness.