Turbulence, low-temperature reactivity, and their couplings as turbulent cool flames are crucial to modern engine designing and low-carbon fuel development. While the flamelet method is a promising solution to turbulent combustion, its applicability and accuracy to cool flames have not been thoroughly comprehended. The objective of the present study is to explore the capability of the steady flamelet method in large eddy simulation (LES) of turbulent cool flames. A laminar counterflow non-premixed cool flame configuration is first simulated on a 2-dimensional grid, showing the good validity of flamelet library setup and table interpolation of the method. Then the application to full-scale turbulent cases of cool combustion is presented with the comparison to the experimental measurements and the referenced direct numerical simulation (DNS) data. This is the first LES of a turbulent cool flame, and the result demonstrates the ability of the method in capturing the mean and variance trends for the temperature, mixture fraction and formaldehyde with good quantitative agreement. Meanwhile, conditional result analysis also shows that this approach in a two-stream flamelet form can describe the three-stream experimental system reasonably well. On this basis, three well-documented reaction mechanisms are employed to examine their performances in flamelet LES of turbulent cool flames. The result reveals that the choice of the chemistry scheme does alter the time-averaged prediction of temperature and formaldehyde, whereas the variance profiles of formaldehyde and mixture fraction are not significantly influenced.