A large eddy simulation (LES) employing a non-adiabatic flamelet generated manifolds (NA-FGM) approach, which can account for the effects of heat loss, is applied to CH4-air super lean premixed combustion fields generated by an axisymmetric jet burner with cooled walls under pressurized conditions. In addition, the validity in predicting the CO emissions is examined. The NA-FGM approach captures the trends of CO emissions well during the experiments, in which the CO emissions increase with a decreasing equivalence ratio. It is shown that the increase in CO emissions for low equivalence ratios is not due to the increase in the CO production, but to the slow rate of CO consumption, which keeps the CO concentration high downstream. The results suggest that capturing such a sensitive reduction of CO consumption rate by heat loss is important for accurately predicting the CO emissions in developing a low-emissions gas turbine combustor at low load.