Machine learning (ML) classifiers are invaluable building blocks that have been used in many fields. High quality training dataset collected from multiple data providers is essential to train accurate classifiers. However, it raises concern about data privacy due to potential leakage of sensitive information in training dataset. Existing studies have proposed many solutions to privacy-preserving training of ML classifiers, but it remains a challenging task to strike a balance among accuracy, computational efficiency, and security. In this paper, we propose Heda, an efficient privacypreserving scheme for training ML classifiers. By combining homomorphic cryptosystem (HC) with differential privacy (DP), Heda obtains the tradeoffs between efficiency and accuracy, and enables flexible switch among different tradeoffs by parameter tuning. In order to make such combination efficient and feasible, we present novel designs based on both HC and DP: A library of building blocks based on partially HC are proposed to construct complex training algorithms without introducing a trusted thirdparty or computational relaxation; A set of theoretical methods are proposed to determine appropriate privacy budget and to reduce sensitivity. Security analysis demonstrates that our solution can construct complex ML training algorithm securely. Extensive experimental results show the effectiveness and efficiency of the proposed scheme.