A lever viscoelastic damping wall assembly includes a first wall, a second wall and a viscoelastic damper. The first and second walls are connected respectively to a first structural member and a second structural member. The viscoelastic damper includes a swing rod connected pivotally to the first and second walls, a first viscoelastic unit connected between the first wall and an end portion of the swing rod, and a second viscoelastic unit connected between the second wall and an opposite end portion of the swing rod. The swing rod is driven to pivot relative to the first and second walls, and to thereby generate shear deformations of the first and second viscoelastic units to damp a relative movement between the first and second structural members.