In order to decrease the resource cost in delay tolerant networks, single-copy forwarding protocols have been proposed by researchers. However, recent research has pointed out that single-copy forwarding protocols lead to great unfairness of the nodes' traffic load and make the highly connected nodes suffer congestion. In order to bridge this gap, a congestion control mechanism based on accepting the threshold is put forward in this paper, which makes each DTN node dynamically adjust to its accepting threshold and accordingly to its congestion state. Moreover, the mechanism can be widely adopted, since it is independent of the forwarding protocols and does not affect the choice of the relay nodes made by the forwarding protocol. In order to validate the proposed mechanism, an algorithm named SimBetCC is proposed, which incorporates the congestion control mechanism with existing SimBet protocol. Experimental results show that SimBetCC can cope with congestion and also outperforms FairRoute with congestion control in many aspects, e.g., the message delivery ratio, the delivery delay.