This study focuses on the effect of pressure level and H2 content in the CH4–H2 fuel mixture on the global consumption-based turbulent flame speed (ST). The data considered in the analysis are collected for a variety of CH4–H2 fuel compositions (from 50% to 100% H2 vol.), pressure levels ranging from 0.5 to 1.5 MPa, and preheating temperatures up to 623.15 K. Different trends of ST/SL0 (SL0 is the adiabatic unstretched laminar flame speed) are observed as a function of the normalized turbulence intensity (u’/SL0), depending on the H2 content in CH4–H2 fuel blends. Yet, for all the CH4–H2 fuel mixtures considered, ST/SL0 consistently increases with H2 content. Rising pressure levels are responsible for larger ST/SL0, in direct proportion with the H2 content. These trends are mostly caused by the decrease in SL0, which causes changes to the characteristics of the flamelet that becomes more sensitive to hydrodynamic wrinkling through the high molecular diffusivity of H2.