In this paper, we propose a new mining task: mining top-k frequent closed patterns of length no less than min-l, where k is the desired number of frequent closed patterns to be mined, and min-l is the minimal length of each pattern. An efficient algorithm, called TFP, is developed for mining such patterns without minimum support. Two methods, closed-node-count and descendant-sum are proposed to effectively raise support threshold and prune FP-tree both during and after the construction of FP-tree. During the mining process, a novel top-down and bottom-up combined FP-tree mining strategy is developed to speed-up support-raising and closed frequent pattern discovering. In addition, a fast hash-based closed pattern verification scheme has been employed to check efficiently if a potential closed pattern is really closed. Our performance study shows that in most cases, TFP outperforms CLOSET and CHARM, two efficient frequent closed pattern mining algorithms, even when both are running with the best tuned min-support. Furthermore, the method can be extended to generate association rules and to incorporate user-specified constraints. Thus we conclude that for frequent pattern mining, mining top-k frequent closed patterns without min-support is more preferable than the traditional min-support-based mining.