This paper deals with the investigation of the performance of the skew or the rectangular patches of the active constrained layer damping (ACLD) treatment for active damping of geometrically nonlinear vibrations of skew doubly curved laminated composite shells. Developing a three-dimensional nonlinear electro-mechanical finite element model, the performance of the patches is examined for different configurations of their placements on the top surface of the skew substrate shells. The investigation reveals that the patches of the ACLD treatment significantly improves the active damping characteristics of the skew doubly curved laminated composite shells over the passive damping for suppressing their geometrically nonlinear vibrations. It is suggested that even though the substrate shells are skew, a rectangular patch of the ACLD treatment located at the centre of the top surface of the substrate shells should be used for achieving optimum damping of geometrically nonlinear vibrations of skew doubly curved laminated composite shells irrespective of the skew angles and boundary conditions. The effects of variations of the piezoelectric fiber orientation angle in the constraining layer of the ACLD patches and the skew angle of the substrate shells on the control authority of the ACLD patches have been extensively investigated.