The flame dynamics in a novel, ultra-lean non-premixed model gas turbine (GT) burner flame was numerically studied using large eddy simulation (LES) coupled with probability density function (PDF) based on the Euler stochastic field (ESF) method. One non-reacting case and three reacting cases with global equivalence ratio ϕglob=1.0,0.6,0.3 were simulated. Comparison of mean flow fields and OH distributions between numerical and experimental results was conducted. Flame dynamics including flame stabilization, structures and transitions of combustion modes were investigated. The simulation results were in close agreements with the experimental measurements showing the capability of PDF-ESF LES model in predicting the flame behaviors. At higher ϕglob, the fuel jet velocity was higher, which yielded higher scalar dissipation rate, χ, near the burner exit, leading to local extinction and flame lifted-off. In the extinction region, a series of relatively low to medium temperature reactions were active, providing favorable conditions for re-ignition downstream where χ is lower than the critical scalar dissipation rate for flame extinction, χcrt. In addition, with ϕglob decreasing, the flame height decreased due to a smaller jet velocity and χ, and thus the mechanism of flame stabilization changed from the swirl-stabilized to the bluff-body stabilized.