As a powerful supplement to the existing wireless communication technology, free-space optical communication helps to achieve ultra-high-speed wireless communication in many important applications such as redundant link, disaster recovery and secure link. However, beam distortion and intensity scintillation caused by atmospheric turbulence severely limits its communication performance through optical links, and there are still many problems in existing turbulent suppression schemes. Here, we propose an easy-implemented anti-turbulence free-space optical communication scheme based on the tunable zero-order Bessel beam, which is able to provide 2 dB to 3 dB power compensation in comparison with the ones employing traditional Gaussian beams. For the worse link environment with water fog, our scheme can still ensure the stability of the communication link when the Gaussian beam link is cut off. In addition, to generate tunable Bessel beams, we propose a method based on non-uniform Fourier transform to achieve accurate and fast light field simulation.