Frequent pattern (itemset) mining in transactional databases is one of the most well-studied problems in data mining. One obstacle that limits the practical usage of frequent pattern mining is the extremely large number of patterns generated. Such a large size of the output collection makes it difficult for users to understand and use in practice. Even restricting the output to the border of the frequent itemset collection does not help much in alleviating the problem. In this paper we address the issue of overwhelmingly large output size by introducing and studying the following problem: mining top-k approximate frequent patterns. The union of the power sets of these k sets should satisfy the following conditions: (1) including itemsets with larger support as many as possible and (2) including itemsets with smaller support as less as possible. An integrated objective function is designed to combine these two objectives. Consequently, we derive the upper bounds on objective function and present an approximate branch-and-bound method for finding the feasible solution. We give empirical evidence showing that our formulation and approximation methods work well in practice.