Metamorphic InxAl1-xAs (xmax > 0.75) buffer layer (MBL) grown on GaAs with an optimized non-linear graded composition profile along the growth direction is proposed for enhanced reduction of misfit dislocation (MD) density in highly mismatched III-V/GaAs metamorphic heterostructures. The equilibrium distributions of MD density throughout such InxAl1-xAs/GaAs MBLs are calculated. The influence of the initial composition (xmin) of MBL and the elastically strained thin GaAs layer embedded into the InxAl1-xAs MBL on the MD density distribution was studied. An optimum value of the inverse step (Δ), representing the difference between the top In content of the InxAl1-xAs MBL and that of a In0.75Al0.25As virtual substrate (VS) grown atop is determined. It was theoretically shown that Δ above 0.04 results in relaxation of the elastic stresses in VS via formation of the MDs, while the lower Δ values allow growing the VS completely free of MDs. Finally, the metamorphic In0.75Al0.25As/graded-InAlAs/GaAs heterostructures differing from each other by only the composition profile of the graded-InAlAs MBL were grown by MBE on GaAs(001) and studied by atomic force microscopy. The structure with proposed optimized non-linear graded (x = 0.05–0.77) MBL demonstrated the ∼ 1.5 times less MD density as compared to that with the convex-graded (x = 0.05–0.81) MBL, which was estimated to be at the level of ∼ 2·107 cm−2.