This paper deals with the analysis of active constrained layer damping (ACLD) of smart skew fuzzy fiber reinforced composite (FFRC) plates. The novel constructional feature of this fuzzy fiber–reinforced composite is that the uniformly aligned carbon nanotubes (CNTs) are radially grown on the circumferential surface of the horizontal carbon fibers. The constraining layer of the ACLD treatment is composed of the vertically/obliquely reinforced 1-3 piezoelectric composites (PZC). A finite element model has been developed for accomplishing the task of the active constrained layer damping of skew fuzzy fiber reinforced composite (FFRC) plates integrated with the patches of such ACLD treatment. Both in-plane and out-of-plane actuations by the constraining layer of the ACLD treatment have been utilized for deriving the finite element model. The analysis revealed that the vertical actuation dominates over the in-plane actuation. Particular emphasis has been placed on investigating the performance of the patches when the orientation angle of the piezoelectric fibers of the constraining layer is varied in the two mutually orthogonal vertical planes. Also, the effects of varying the skew angle of the substrate composite plates and different boundary conditions on the performance of the patches have been studied. The analysis reveals that the vertically and the obliquely reinforced 1-3 PZC materials should be used for achieving the best control authority of the ACLD treatment according as the boundary conditions of the smart skew laminated composite plates are simply supported and clamped-clamped, respectively.