A double-screen rotary shaft structure includes two synchronous spiral channels disposed on the link shafts. Asynchronous assembly is slidably pivotally fitted on the two link shafts. Two bosses are disposed on the synchronous assembly and respectively inlaid in the spiral channels of the link shafts. Two connection members are respectively securely connected with the two link shafts. Two link assemblies are respectively pivotally fitted on the link shafts to synchronously move with the synchronous assembly. Two slide members are attached to lower sides of the connection members and formed with oblique slots. A guide slide connection member is disposed in each oblique slot and connected with the link assembly. The middle sections of two links are pivotally disposed on the connection members. Each link has a driving end pivotally connected with the link assembly and a driven end to drive the slide member.