Traditional Insurance, a popular approach of financial risk management, has suffered from the issues of high operational costs, opaqueness, inefficiency and a lack of trust. Recently, blockchain-enabled "parametric insurance" through authorized data sources (e.g., remote sensing and IoT) aims to overcome these issues by automating the underwriting and claim processes of insurance policies on a blockchain. However, the openness of blockchain platforms raises a concern of user privacy, as the private user data in insurance claims on a blockchain may be exposed to outsiders. In this paper, we propose a privacy-preserving parametric insurance framework based on succinct zero-knowledge proofs (zk-SNARKs), whereby an insuree submits a zero-knowledge proof (without revealing any private data) for the validity of an insurance claim and the authenticity of its data sources to a blockchain for transparent verification. Moreover, we extend the recent zk-SNARKs to support robust privacy protection for multiple heterogeneous data sources and improve its efficiency to cut the incurred gas cost by 80%. As a proof-of-concept, we implemented a working prototype of bushfire parametric insurance on real-world blockchain platform Ethereum, and present extensive empirical evaluations.