Experimental and numerical study on hydrogen-air flames at elevated pressures and temperatures was conducted. Meanwhile, the calculation is extended to initial pressure and temperature up to 8.0 MPa and 950 K, respectively. Laminar burning velocities and Markstein lengths were obtained at the elevated pressures and temperatures. Sensitivity analysis and flame structure were also analyzed. The results show good agreement between the computed results and experimental data. The study shows that laminar burning velocities are increased with the increase of initial temperature, and they decrease with the increase of initial pressure. With the increase of initial pressure, advancement of the onset of cellular instability is presented and Markstein length is decreased, indicating an increase of flame instability with the increase of initial pressure. The study shows insensitivity of flame instability to initial temperature. Laminar burning velocity is depended on the competition between the main chain branching reactions and chain termination reaction. The chain branching reactions are the temperature-sensitive reaction, while the termination reaction is the temperature-insensitive reaction. Through the extraction of the overall reaction orders, it is demonstrated that with increasing pressure, the overall reaction orders give a decreasing trend and then increasing trend. This behavior suggests an analogy to three explosion limits of hydrogen/oxygen mixtures. Numerical study also shows that the suppression (or enhancement) of overall chemical reaction with the increase of initial pressure (or temperature) is closely linking to the decrease (or increase) of H, O and OH mole fractions in the flames. Strong correlation is existed between burning velocity and maximum radical concentrations of H and OH radicals in the reaction zone of premixed flames. On the basis of the numerical data, an empirical formula for laminar burning velocity is correlated for the hydrogen-air premixed mixture at elevated pressures and temperatures. The correlated laminar burning velocities are in good agreement with the known experimental results and simulated results with CHEMKIN. The correlation can be used in the calculation of laminar burning velocities at evaluated pressures and temperatures.