This paper proposes a privacy-preserving distributed Kalman filter (PP-DKF) to protect the private information of individual network agents from being acquired by honest-but-curious (HBC) adversaries. The proposed approach endows privacy by incorporating noise perturbation and state decomposition. In particular, the PP-DKF provides privacy by restricting the amount of information exchanged with decomposition and concealing private information from adversaries through perturbation. We characterize the performance and convergence of the proposed PP-DKF and demonstrate its robustness against perturbation. The resulting PP-DKF improves agent privacy, defined as the mean squared estimation error of private data at the HBC adversary, without significantly affecting the overall filtering performance. Several simulation examples corroborate the theoretical results.