Aircraft wake is one of the important factors restricting the flight interval between two aircraft in the airport. However, current numerical simulation methods and empirical models cannot take the timeliness and accuracy of the wake evolution at the same time, which is not conducive to the control of airport wake interval. Considering that the aircraft wake is dominated by aircraft wake vortex pairs, whose dynamic instability is the main mechanism of aircraft wake vortex dissipation, this study proposes a fast simulation method for aircraft wake vortex pair instability based on the curvature corrected vortex filament method. Through cubic spline interpolation, the midpoint coordinates of vortex segments are extracted to treat the straight vortex segments as curved ones, and the induced effects of vortex segments on their own control points are also considered, thus the curvature correction of induced velocity in the vortex filament method is realized. The treatment of period conditions in simulating the vortex pair is given, which greatly improves the accuracy of aircraft wake vortex instability prediction. The results of numerical experiments show that, the curvature corrected vortex filament method can make a fast prediction of the long wave instability of aircraft wake vortex pairs at a low cost, and the instability growth rate and inclination angle of the vortex filaments are in good agreement with the theoretical values. When turbulence with different intensities is applied, the dissipation time of vortex pairs simulated by the present method is in good agreement with the theoretical prediction. Particularly, the present method is more accurate for turbulence with moderate or weak intensity.