A two-dimensional direct numerical simulation is performed to investigate the flame structure of $CH_4/N_2-Air$ counterflow nonpremixed flame interacting with a single vortex. The detailed transport properties and a modified 16-step augmented reduced mechanism based on Miller and Bowman#s detailed reaction mechanism are adopted in this calculation. To quantify the strain on flame induced by a vortex, a scalar dissipation rate (SDR) is introduced. The results show that fuel-side and air-side vortex cause an unsteady extinction. In this case, the flame interacting with a vortex is extinguished at much larger SDR than steady flame. It is also found that air-side vortex extinguishes a flame more rapidly than fuel-side vortex. The unsteady effect induced by flame-vortex interaction does not lead to a transient OH overshoot of the maximum steady concentration observed in experiment, while $HO_2$ radical increases more than the maximum steady concentration with increasing SDR. In addition, it is seen that NO and $NO_2$ are not sensitive to the unsteady variation of SDR.