Flame development along a straight vortex was studied experimentally to elucidate the effects of the maximum circumferential velocity and the density, ratio of the flame. A pair of straight vortices was produced in nitrogen-diluted stoichiometric hydrogen-oxygen mixtures with density ratios ranging from 5.3 to 7.2. The velocity field measured by particle image velocimetry (PIV) showed that the vortex tube had a mean maximum circumferential velocity ranging from 18.0 to 35.8 m/s and had a mean core diameter ranging from 5 to 6 mm. One of the vortices was ignited at the core by a focused laser at 193 nm without disturbing the flow field. The flame propagated along the axis of the straight vortex at a speed much higher than in the radial direction or in the quiescent mixture, The axial propagation velocity increased over time and became nearly constant when the half-axial length of the flame was larger than the core diameter of the vortex tube. The axial propagation velocity at steady state, us roughly proportional to the Maximum circumferential velocity and to the density ratio minus unity. The axial propagation velocity in the initial stage increased with the square root of the half-axial length of the flame as well as with the maximum circumferential velocity and the density ratio minus unity.