Open-access blockchains based on proof-of-work protocols have gained tremendous popularity for their capabilities of providing decentralized tamper-proof ledgers and platforms for data-driven autonomous organization. Nevertheless, the proof-of-work based consensus protocols are vulnerable to cyber-attacks such as double-spending. In this paper, we propose a novel approach of cyber risk management for blockchain-based service. In particular, we adopt the cyber-insurance as an economic tool for neutralizing cyber risks due to attacks in blockchain networks. We consider a blockchain service market, which is composed of the infrastructure provider, the blockchain provider, the cyber-insurer, and the users. The blockchain provider purchases from the infrastructure provider, e.g., a cloud, the computing resources to maintain the blockchain consensus, and then offers blockchain services to the users. The blockchain provider strategizes its investment in the infrastructure and the service price charged to the users, in order to improve the security of the blockchain and thus optimize its profit. Meanwhile, the blockchain provider also purchases a cyber-insurance from the cyber-insurer to protect itself from the potential damage due to the attacks. In return, the cyber-insurer adjusts the insurance premium according to the perceived risk level of the blockchain service. Based on the assumption of rationality for the market entities, we model the interaction among the blockchain provider, the users, and the cyber-insurer as a two-level Stackelberg game. Namely, the blockchain provider and the cyber-insurer lead to set their pricing/investment strategies, and then the users follow to determine their demand of the blockchain service. Specifically, we consider the scenario of double-spending attacks and provide a series of analytical results about the Stackelberg equilibrium in the market game.