Light beams carrying orbital angular momentum (OAM) have been constantly developing in free-space optical (FSO) communications. However, perturbations in the free space link, such as rain, fog, and atmospheric turbulence, may affect the transmission efficiency of this technique. If the FSO communications procedure takes place in a smoke condition with low visibility, the communication efficiency also will be worse. Here, we use deep learning methods to recognize OAM eigenstates and superposition states in a thick smoke condition. In a smoke transmission link with visibility about 5 m to 6 m, the experimental recognition accuracy reaches 99.73% and 99.21% for OAM eigenstates and superposition states whose Bures distance is 0.05. Two 6 bit/pixel pictures were also successfully transmitted in the extreme smoke conditions. This work offers a robust and generalized proposal for FSO communications based on OAM modes and allows an increase of the communication capacity under the low visibility smoke conditions.