Mining frequent itemsets in transaction databases is an important task in many applications. It becomes more challenging when dealing with a large transaction database because traditional algorithms are not scalable due to the memory limit. In this paper, we propose a new approach for approximately mining of frequent itemsets in a big transaction database. Our approach is suitable for mining big transaction databases since it produces approximate frequent itemsets from a subset of the entire database, and can be implemented in a distributed environment. Our algorithm is able to efficiently produce high-accurate results, however it misses some true frequent itemsets. To address this problem and reduce the number of false negative frequent itemsets we introduce an additional parameter to the algorithm to discover most of the frequent itemsets contained in the entire data set. In this article, we show an empirical evaluation of the results of the proposed approach.