The analytical formula of the probability density of a single orbital angular momentum (OAM) mode for pin-like optical vortex beams (POVBs) in turbulent atmosphere is derived. Its OAM spectrum in the receiving plane is obtained by the numerical calculation. For comparison, the OAM spectrum of commonly Gaussian vortex beams is showed, too. Those results show that POVBs show good performance on resisting the cross talk of the OAM mode induced by the turbulence in some cases, such as smaller radius of the receiving aperture, longer propagation distance, and stronger turbulence. Our finding has application in free-space optical communication based on the OAM mode.