The obstacle in a channel is a typical scenario for free-space optical (FSO) communications, however, it will destroy the information in channels, especially for the orbital angular momentum (OAM) multiplexing systems and cause performance degradation. Motivated by the feature of predefining intensity profile, here we propose to use frozen wave (FW) carrying OAM for the FSO communications to mitigate the influence of obstacles on the beam propagation. The key idea is to design the longitudinal intensity profile of FW to distribute the beam energy of the location where the obstacle exists over a large region and focus again on the central region after the obstacle for propagation. By analyzing the cases under different sizes, positions, and shapes of the obstacles with on-axis and off-axis scenarios, it has been demonstrated that the detection probability of OAM mode carried by FW can be improved by 0.35 and 0.15 in short-distance and long-distance transmission scenarios, respectively, when compared to that carried by Bessel-Gaussian beam. It demonstrates the FWs have great potential in the OAM-based FSO communications, especially for the obstacle channels.