We study the spectral density of vortex beams propagating in atmospheric turbulence by numerical simulation and experiment with a spatial light modulator (SLM). It is found that the figures produced by experiment with SLM are quite different from those by traditional numerical simulation. In view of this, we put forward a new simulation method that refers to the theory of beam wander, leading to a consistency between numerical simulation and experimental results eventually. The improved simulation method could improve the accuracy of beam simulation greatly in optical study.