The　band　structure　of　torsional　vibration　in　a　2-D　discrete　gyroscope　phononic　crystal　was　studied.　The　unit　cell　consists　of　a　gyroscope,　frame,　and　torsional　springs.　The　governing　equations　of　the　unit　cell　and　the　dispersion　relationship　were　derived　using　the　angular　momentum　theorem　and　Bloch＇s　theorem,　respectively,　and　the　characteristics　of　band　structure　were　also　analyzed.　The　effects　of　critical　parameters　on　the　band　structure,　such　as　angular　momentum,　moment　inertia,　and　torsional　stiffness,　were　studied　theoretically.　Moreover,　the　band　structure　was　also　calculated　by　numerical　method,　and　the　results　agree　well　with　the　theoretical　prediction,　which　validates　the　existence　of　band　gap　in　this　phononic　crystal.　©　2019　Journal　of　Dynamics　and　Control.　All　rights　reserved.