This paper deals with a study on the active constrained layer damping (ACLD) of geometrically nonlinear vibrations of functionally graded (FG) laminated composite plates. The constraining layer of the ACLD treatment is considered to be made of the vertically/obliquely reinforced 1-3 piezoelectric composites (PZCs). The substrate FG laminated composite plate is composed of generally orthotropic FG layers. The generally orthotropic FG layer is a fiber reinforced composite layer in which the fibers are longitudinally aligned in the plane parallel to the top and bottom surfaces of the layer and their orientation angle is assumed to vary in the thickness direction according to a simple power-law in order to make it as a graded layer only in the thickness direction. The constrained viscoelastic layer of the ACLD treatment is modeled by implementing the Golla-Hughes-McTavish (GHM) method. Based on the first order shear deformation theory, the finite element (FE) model is developed to model the open-loop and closed-loop nonlinear dynamics of the overall FG laminated composite plates integrated with a patch of such ACLD treatment. The analysis suggests the potential use of the ACLD treatment with its constraining layer made of the vertically/obliquely reinforced 1-3 PZC material for active control of geometrically nonlinear vibrations of FG laminated composite plates. The effect of piezoelectric fiber orientation in the active 1-3 PZC constraining layer on the damping characteristics of the overall FG laminated composite plates is also investigated.