This study has numerically modeled the stabilization and combustion processes of turbulent lifted methane-air premixed flames on low-swirl burners (LSB). In these turbulent swirling premixed flames, tangentially injected air jets induce a turbulent swirling flow which plays a crucial role in stabilizing the lifted turbulent flames. In the present approach, the turbulence-chemistry interaction is represented by the level-set-based flamelet model. Two- and three-dimensional computations have been made for various swirl numbers and nozzle lengths. In terms of the center line axial velocity, mean progress variable, rms axial velocity fluctuations, and local equivalence ratios, numerical results are compared with experimental data. The three-dimensional approach, compared to the two-dimensional approach, yields a much better conformity with measurements without any analytic assumptions on the inlet swirl profiles. Numerical results indicate clearly that the present level-set-based flamelet approach has realistically simulated the structure and stabilization mechanism of the lifted turbulent stoichiometric and lean methane-air premixed flames on the low-swirl burner.