The turbulent flow of spatially developing and high-speed hydrogen/air mixing layers subject to small skew angle ζ is systematically investigated by means of direct numerical simulation. The present database features both detailed chemistry and detailed transport (i.e., Soret, Dufour, and bulk viscosity effects). The angle ζ measures the misalignment of the two asymptotic streams of fluid, whose interaction creates the turbulent mixing region. Numerical simulations have been carried out either in the absence of skewing, namely, perfectly parallel streams (ζ=0°), or in skew angles ζ=5°, 10°, and 15°. The streamwise evolution and the self-similar state of turbulence statistics of skewed cases are reported and compared to the unskewed and reference case. The present computations indicate that the transitional region and the fully developed turbulence region depends strongly on the degree of flow skewing at the inlet. In particular, we find that skewing yields faster growth of the inlet structures, thus leading to mixing enhancement. The underlying mechanisms responsible for turbulence modulation are analyzed through the transport equation of the Reynolds stresses. One possible perspective of the present work concerns the mixing control and a reliable comparison between the experiment, simulations, and turbulence modeling.