In this study, first ply failure (FPF) analysis of multi-walled carbon nanotubes (MWCNTs)/epoxy/glass fiber laminated curved composite panels with various taper configuration under transverse uniform pressure load distributed over the panel surface has been performed. In this regard, various failure criterion were considered, including Hoffman, Tsai–Wu, Tsai–Hill, and maximum stress, to investigate the numerical FPF load using finite element (FE) formulation with displacement fields derived from high order shear deformation theory (HSDT) with displacement field having seven degrees of freedom. The effectiveness of the proposed formulation was validated by comparing the numerically predicted FPF load with experimentally obtained FPF load using a universal testing machine from displacement/strain measurement. Finally, the effects of aspect ratio, different weight fraction of MWCNTs, taper configuration, curved geometry, and aspect ratio on the FPF load of the laminated tapered composite panels are studied. The numerical and experimental studies of the first ply failure behavior have demonstrated that the use of MWCNTs ensures a significant improvement in the FPF load of the analyzed laminated tapered curved composite panels. The taper configuration 3 (TC-3) with hyperbolic curved geometry exhibited the highest resistance to failure than taper configuration 1 (TC-1) and taper configuration 2 (TC-2). Moreover, the aforementioned parameters significantly influence the FPF load of laminated curved panels with various taper configurations. Furthermore, this study can be effectively used as a benchmark problem for researchers and as a tool to design practical laminated tapered curved composite panels with sufficient accuracy.