Optical beam wander is one of the most important issues for free-space optical (FSO) communication. We theoretically derive a beam wander model for Bessel beams propagating in turbulent atmosphere. The calculated beam wander of high order Bessel beams with different turbulence strengths are consistent with experimental measurements. Both theoretical and experimental results reveal that high order Bessel beams are less influenced by the turbulent atmosphere. We also demonstrate the Bessel beams based orbital angular momentum (OAM) multiplexing/demultiplexing in FSO communication with atmospheric turbulence. Under the same atmospheric turbulence condition, the bit error rates of transmitted signals carried by high order Bessel beams show smaller values and fluctuations, which indicates that the high order Bessel beams have an advantage of mitigating the beam wander in OAM multiplexing FSO communication.