Differential quadrature method (DQM) was used to compute the critical buckling load (CBL) of composite laminates containing complex delamination shapes. The composite laminate was initially flat; however, it buckled under a compressive load due to weak adhesive between the outer ply and the whole composite laminate. Previous data obtained for composite laminates containing circular or elliptical delaminations by finite element and the Rayleigh-Ritz methods as well as DQM available in the literature were used to validate the accuracy of the approach. A good agreement between the results was observed. To show the ability of this approach for calculating the CBL of a composite laminate containing complex delamination shape, a crescent-shaped delamination was considered. The CBLs for various stacking sequences of such a composite laminate were then calculated and discussed. The commercial finite element package, ABAQUS was used to validate the DQM results for crescent delamination.