At the peak of bitcoin transactions, users need to increase the transaction fee to compete for the limited block space in order to pack the transactions into the block as soon as possible. An optimal transaction fee payment strategy was proposed to solve the problem of how to choose the appropriate transaction fees. First, the process of transactions queueing to complete for going up on the blockchain was modeled to a non-preemptive queueing model with priority by adopting the queuing game theory. Then, the impact of transaction fee on transaction time was analyzed, so as to obtain the functional relation between transaction time and transaction fee, and the Nash equilibrium payment strategy for the user was derived. Simulation results showed that the user total cost (weighted sum of the waiting time and the transaction fee) was able to be effectively reduced when the optimal payment strategy was adopted. Compared with the strategy of not paying transaction fees and the strategy of linearly increasing transaction fees according to the congestion, the proposed strategy had the user total cost decreased by 97% and 72% respectively in the system with high load. The proposed payment strategy can effectively reduce the cost of transaction fees while ensuring that the transactions are processed as quickly as possible.