Lock-based thread synchronization techniques have been commonly used in parallel programming on multi-core processors. However, lock can cause deadlocks and poor scalabilites, and Transactional Memory (TM) has been proposed and studied for lock-free synchronization. On TMs, transactions are executed speculatively as long as there is no conflict on shared variables. On HTMs, which are the hardware implementations of TM, if a speculative execution of a transaction fails, the re-execution of the transaction should wait a period prescribed by a backoff algorithm to avoid further conflicts. However, the performance of HTM may be decreased drastically by wastefully long backoff periods. To address this problem, in this paper, we propose a new algorithm to set a value called Priority on each transaction, and the transaction which should be aborted is selected according to Priority instead of the initiated time of transactions. The result of the experiment shows that the execution time of HTM is reduced 59.9% in maximum, and 11.2% in average with 16 threads.