The unsteady evolution of lifted methane–air jet flames following spark ignition is computed using Large Eddy Simulation (LES). A presumed joint Probability Density Function (PDF) approach is used for the sub-grid combustion modelling accounting for both premixed and non-premixed mode contributions. Two flames, one with high and another with low jet velocities are investigated and the computed temporal variation of flame leading point agrees quite well with the measured data for both the transient evolution and final lift-off height. The joint PDF of the axial and radial stabilisation locations shows that these locations are correlated with the jet exit velocity. The flame leading point evolution in the three-dimensional physical space is visualised using its trajectory, starting from the ignition location to the final lift-off height. A spiral-shaped path is observed for both velocity cases showing different flame propagation behaviours at different heights from the jet exit. These observations are explained on a physical basis.