Miners in a blockchain system are suffering from ever-increasing storage costs, which in general have not been properly compensated by the users’ transaction fees. This reduces the incentives for the miners’ participation and may jeopardize the blockchain security. To mitigate this blockchain insufficient fee issue, we propose a Fee and Waiting Tax (FWT) mechanism, which explicitly considers the two types of negative externalities in the system. Specifically, we model the interactions between the protocol designer, users, and miners as a three-stage Stackelberg game. By characterizing the equilibrium of the game, we find that miners neglecting the negative externality in transaction selection cause they are willing to accept insufficient-fee transactions. This leads to the insufficient storage fee issue in the existing protocol (i.e., deployed in Bitcoin and Ethereum). Moreover, our proposed optimal FWT mechanism can motivate users to pay sufficient transaction fees to cover the storage costs and achieve the unconstrained social optimum. Numerical results show that the optimal FWT mechanism guarantees sufficient transaction fees and achieves an average social welfare improvement of 51.43% or more over the existing protocol. Furthermore, the optimal FWT mechanism reduces the average waiting time of low-fee transactions and all transactions by 68.49% and 61.56%, respectively.