In this paper, an efficient strategy for mining top-K non-trivial fault-tolerant repeating patterns (FT-RPs in short) with lengths no less than min_len from data sequences is provided. By extending the idea of appearing bit sequences, fault-tolerant appearing bit sequences are defined to represent the locations where candidate patterns appear in a data sequence with insertion/deletion errors being allowed. Two algorithms, named TFTRP-Mine(Top-K non-trivial FT-RPs Mining) and RE-TFTRP-Mine (REfinement of TFTRP-Mine), respectively, are proposed. Both of these two algorithms use the recursive formulas to obtain the fault-tolerant appearing bit sequence of a pattern systematically and then the fault-tolerant frequency of each candidate pattern could be counted quickly. Besides, RE-TFTRP-Mine adopts two additional strategies for pruning the searching space in order to improve the mining efficiency. The experimental results show that RE-TFTRP-Mine outperforms TFTRP-Mine algorithm when K and min_len are small. In addition, more important and implicit repeating patterns could be found from real music objects by adopting fault tolerant mining.