•The BSM-Ether combines selfish mining and bribery attacks in Ethereum.•We analyze the mining rewards and the impact of bribes on the rewards for parties.•The simulation of BSM-Ether is performed and results are analyzed. Blockchain-enabled distributed networks present a new infrastructure for building reliable and privacy-preserving healthcare utilities. Among them, Ethereum networks have gained specialized attention for their high usability and security. In this paper, we raise the awareness of Ethereum’s vulnerability due to selfish mining, in which ill-disposed miners are feasible to receive more rewards than honest ones. To demonstrate this, we compose a new bribery selfish mining scheme, the BSM-Ether, targeted to Ethereum. The BSM-Ether attack can be easily conducted and has higher rewards than other existing malicious attacks. Besides, we present a formal and rigorous analysis of multiple kinds of rewards from the BSM-Ether attack. Simulation experiments show the high effectiveness of BSM-Ether – the attacker can get a higher revenue with few efforts. To tackle this variability, we present some implementation level proposals and suggestions for building healthcare systems on top of Ethereum to minimize the negative effect of the security deficiency of underlying systems.