With the widespread adoption of blockchain technology, the transaction fee mechanism (TFM) in blockchain systems has become a prominent research topic. An ideal TFM should satisfy user incentive compatibility (UIC), miner incentive compatibility (MIC), and miner-user side contract proofness (c-SCP). However, state-of-the-art works either fail to meet these three properties simultaneously or only satisfy them under certain conditions. In this paper, we propose a burning N-price auction TFM named BNP. This mechanism divides the transaction fee into a base fee, which is burned, and a priority fee, which is allocated to miners. Theoretical proofs and experimental analyses demonstrate that, even under conditions of significant transaction congestion, this mechanism satisfies UIC, MIC, and c-SCP simultaneously. Furthermore, the BNP mechanism is not constrained by the type of blockchain consensus, making it widely applicable.