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This paper investigates the problem of multi-user multichannel access in distributed high-frequency (HF) diversity communication networks using a game-theoretic learning algorithm which is based on correlation equilibrium (CE). We formulate the channel access problem in the HF networks as a non-cooperative game. In the access game, each user equipment (UE) optimizes its access strategy without the information about other UEs, which makes the channel access problem challenging. It is proved that there is at least one CE point that makes all UEs' access strategy efficient and fair. We propose a distributed learning algorithm based on CE to achieve multi-user access with low cost and fairly in the distributed HF networks. We use coordination signals to help each UE learn the access strategy by themselves. When each UE receives and recognizes the right coordination signals, UEs will learn to transmit data on right channels without further collisions after the learning phase. The simulation results show that the proposed learning algorithm can not only completely avoid interference and get optimal throughput but also guarantee fairness among all UEs.