In this paper, we propose a training algorithm of support vector machine (SVM) with a sensitive variable. Although machine learning models enable automatic decision making in the real world applications, regulations prohibit sensitive information from being used to protect privacy. In particular, the privacy protection of the legally protected attributes such as race, gender, and disability is compulsory. We present an efficient least square SVM (LSSVM) training algorithm using a fully homomorphic encryption (FHE) to protect a partial sensitive attribute. Our framework posits that data owner has both non-sensitive attributes and a sensitive attribute while machine learning service provider (MLSP) can get non-sensitive attributes and an encrypted sensitive attribute. As a result, data owner can obtain the encrypted model parameters without exposing their sensitive information to MLSP. In the inference phase, both non-sensitive attributes and a sensitive attribute are encrypted, and all computations should be conducted on encrypted domain. Through the experiments on real data, we identify that our proposed method enables to implement privacy-preserving sensitive LSSVM with FHE that has comparable performance with the original LSSVM algorithm. In addition, we demonstrate that the efficient sensitive LSSVM with FHE significantly improves the computational cost with a small degradation of performance.