State of health (SOH) estimation is essential for life evaluation and health management of lithium-ion battery (LIB). This paper proposes a novel SOH estimator by using the partial constant-voltage (CV) charging data. First, a thorough analysis is performed over different CV health indicators (HIs) in terms of the HI-SOH correlation as well as the robustness to CV partialness and disturbances, and the CV capacity is proved to be more informative and robust for SOH estimation. Second, to tackle the practical challenge arising from CV charging partialness, a novel CV phase reconstruction method combining Q-V modeling and open-circuit voltage (OCV) estimation iteratively is proposed to predict the CV capacity authentically based on the available partial CV data. The extracted CV capacity is further used to estimate the battery SOH precisely. The proposed method is validated with long-term degradation experiments performed on NCA cells. Results suggest that the proposed method manifests itself with a high estimation accuracy, a low requirement on the charging completeness, and a high robustness to cell inconsistency.