Frequently used items mining is a significant subject of data mining studies. In the last ten years, due to innovative development, the quantity of data has grown exponentially. For frequent Itemset (FIs) mining applications, it imposes new challenges. Misconceived information may be found in recent algorithms, including both threshold and size based algorithms. Threshold value plays a central role in generating frequent itemsets from the given dataset. Selecting a support threshold value is very complicated for those unaware of the dataset’s characteristics. The performance of algorithms for finding FIs without the support threshold is, however, deficient due to heavy computation. Therefore, we have proposed a method to discover FIs without the support threshold, called Top-k frequent itemsets mining (TKFIM). It uses class equivalence and set-theory concepts for mining FIs. The proposed procedure does not miss any FIs; thus, accurate frequent patterns are mined. Furthermore, the results are compared with state-of-the-art techniques such as Top-k miner and Build Once and Mine Once (BOMO). It is found that the proposed TKFIM has outperformed the results of these approaches in terms of execution and performance, achieving 92.70, 35.87, 28.53, and 81.27 percent gain on Top-k miner using Chess, Mushroom, and Connect and T1014D100K datasets, respectively. Similarly, it has achieved a performance gain of 97.14, 100, 78.10, 99.70 percent on BOMO using Chess, Mushroom, Connect, and T1014D100K datasets, respectively. Therefore, it is argued that the proposed procedure may be adopted on a large dataset for better performance.