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This paper addresses a novel fuzzy-based distributed behavioural control with the wall-following strategy for robot swarm navigation in arbitrary-shaped environments. Instead of avoiding large-sized obstacles during the swarm navigation, the proposed fully distributed control enables the robot swarm to transform from aggregation configuration to one-chain configuration and follow the obstacle boundary to overcome it. The wall-following strategy and one-chain configuration empower the swarm navigation to avoid local minima caused by obstacles and connectivity maintenance without dealing with the alignment control of swarm behaviours. The fuzzy-logic control is applied to calculate the parameters of the distributed control strategies. The proposed method is examined and evaluated in both simulation and real experiments.