Background: Genomic data have been collected by different institutions and companies and need to be shared for broader use. In a cross-site genomic data sharing system, a secure and transparent access control audit module plays an essential role in ensuring the accountability. The 2018 iDASH competition first track provides us with an opportunity to design efficient logging and querying system for cross-site genomic dataset access audit. We designed a blockchain-based log system which can provide a light-weight and widely compatible module for existing blockchain platforms. The submitted solution won the third place of the competition. In this paper, we report the technical details in our system. Methods: We present two methods: baseline method and enhanced method. We started with the baseline method and then adjusted our implementation based on the competition evaluation criteria and characteristics of the log system. To overcome obstacles of indexing on the immutable Blockchain system, we designed a hierarchical timestamp structure which supports efficient range queries on the timestamp field. Results: We implemented our methods in Python3, tested the scalability, and compared the performance using the test data supplied by competition organizer. We successfully boosted the log retrieval speed for complex AND queries that contain multiple predicates. For the range query, we boosted the speed for at least one order of magnitude. The storage usage is reduced by 25%. Conclusion: We demonstrate that Blockchain can be used to build a time and space efficient log and query genomic dataset audit trail. Therefore, it provides a promising solution for sharing genomic data with accountability requirement across multiple sites.