Consensus algorithms play a critical role in blockchains and directly impact their performance. During consensus processing, nodes need to validate and order the pending transactions into a new block, which requires verifying the application-specific data encapsulated within a transaction. This exposes the underlying data to the consensus nodes, presenting privacy concerns. Existing consensus algorithms focus on realizing application security and performance goals, but lack privacy-by-design properties or are resource-heavy and intended for securing permissionless blockchain networks. In this paper, we propose P-CFT, a zero-knowledge and crash fault tolerant consensus algorithm for permissioned blockchains. The proposed consensus algorithm provides inherent data privacy directly to the consensus layer, while still providing guarantees of crash fault tolerance. We conduct experiments using the Hyperledger Ursa cryptographic library, and the results show promise for integrating P-CFT into existing permissioned blockchain systems requiring privacy-preserving and crash fault tolerant features.