Frequent itemset mining is a very important problem in data mining. Closed frequent itemsets is the condensed representation of frequent itemsets thus spend less memory, so it is much suitable for stream mining. But on the other hand, when the minimum support is much lower, the size of closed frequent itemsets turns larger, which makes the performance reduced a lot. In this paper, we introduce a threshold to approximately mine closed frequent itemsets with a limited error tolerance. A new algorithm named ACFIM is proposed based on the introduction of the distance conception to mine the sliding window of stream, in which more data are pruned and more computation time are saved, so it much raise the performance in running time and memory comparing to the state-of-art closed frequent itemsets mining methods. Our experimental results over real-life datasets show that ACFIM is effective and efficient.