Frequent-Regular pattern mining has been introduced to extract interesting patterns based on their occurrence behavior. This approach considers the terms of frequency and regularity to determine significant of patterns under user-given support and regularity thresholds. However, it is well-known that setting of thresholds to discover the most interesting results is a very difficult task and it is more reasonable to avoid specifying the suitable thresholds by letting users assign only simple parameters. In this paper, we introduce an alternative approach, called Top-k frequent/regular pattern mining based on weights of interests, which allows users to assign two simple parameters: (i) a weight of interest on frequency/regularity and (ii) a number of desired patterns. To mine patterns, we propose an efficient single-pass algorithm, TFRP-Mine, to quickly mine patterns with frequent/regular appearance. Experimental results show that our approach can effectively and efficiently discover the valuable patterns that meet the users' interest.