Large eddy simulations (LES) have been carried out to calculate turbulent flame propagation in a fan-stirred combustion bomb and a Bunsen-type burner. Objective of the work is to reveal the main mechanism of increased flame wrinkling due to elevated pressure and to assess the ability of the turbulent flame-speed closure (TFC-class) combustion model to reproduce the enhancement of flame wrinkling or burning rate at elevated pressures. The simulations have been performed for a premixed methane/air mixture at equivalence ratio 0.9 and the pressure has been varied from 1 bar to 5 bar. The turbulent kinetic energy is found to increase with pressure in the high frequency range, indicating reinforced small-scale turbulent fluctuations at elevated pressure. The reason is attributed to the increased turbulent Reynolds number with pressure, which shifts the turbulent energy spectra to the higher wave number range. A reinforced flame wrinkling and an increased total burning rate are obtained at elevated pressure, which is in accordance with results from previous high-pressure combustion experiments. In addition, applying the same method to a quiescent flow in the bomb vessel reveals a decrease of the overall burning rate with pressure, which agrees with the behaviour of laminar flame speed at elevated pressures. ... mehrTherefore, the beneficial effect of increased burning rate or flame wrinkling at elevated pressure can be explained by the enhanced small-scale turbulent fluctuations along with formation of small-scale vortices and flame structures, which over-compensate the reduced local laminar burning velocity at high pressures. The calculated amplification rates of flame wrinkling factor at increased pressures show a reasonable agreement with measured data for both fan-stirred bomb and Bunsen flame configurations, without using any additional adjusting parameters for considering the pressure effect. The results justify the applicability of the current TFC-LES method for high-pressure combustion processes.