Mutation Based Fault Localization (MBFL) is a recently proposed approach with the advantage of high fault localization accuracy but limited to actual use in industry area since its huge mutation execution cost. Researchers improve MBFL’s execution efficiency from three aspects: reducing the number of mutants, reducing the number of test cases, and optimizing the mutant’s execution process. The former two methods were studied a lot and showed promising results, but in terms of reducing the number of test cases during MBFL, the related studies were limited for losing the precision of fault localization. In this study, we propose an Information Entropy based Test Cases Reduction strategy (IETCR) for MBFL. IETCR first calculates the information entropy of test cases, then sorts them according to the information entropy. Finally, it selects a small number of valuable test cases to execute mutants. Empirical studies are conducted on 100 fault versions of 6 programs from the SIR repository. The results show that IETCR can reduce 56.3%–88.6% mutation execution cost while keeping almost the same fault localization accuracy with the original MBFL.