Fault localization is an expensive phase of software debugging processes. Although Mutation-based Fault Localization (MBFL) is a promising technique, its computational cost remains high due to the extensive mutation executions involved in mutation analysis. Previous studies have primarily focused on reducing costs by decreasing the mutant numbers and optimizing the execution, yielding promising results. However, test case reduction has also proven to be effective in reducing costs in MBFL. In this paper, we propose an approach called Contribution-Based Test Case Reduction (CBTCR) aimed at enhancing MBFL efficiency. CBTCR assesses the contribution value of each test case and selects them accordingly. The reduced test suite is then used for mutant execution. We evaluate CBTCR on 543 real software faults from Defects4J benchmark. Results show that CBTCR outperforms other MBFL test case reduction strategies (e.g. FTMES, IETCR), in terms of the Top-N and MAP metrics. Moreover, CBTCR achieves an average cost reduction of 87.06%, while maintaining accuracy comparable to those of the original MBFL techniques. This research paper presents an innovative and effective solution for optimizing MBFL, which can significantly reduce the cost and time required for software debugging.