Over the past decades, face recognition has been a problem of critical interest in the machine learning and signal processing communities. However, conventional approaches such as eigenfaces do not protect the privacy of user data, which is emerging as an important design consideration in today's society. In this work, we leverage a supervised-learning subspace projection method called Discriminant Component Analysis (DCA) for privacy-preserving face recognition. By projecting the data onto the lower-dimensional signal subspace prescribed by DCA, high performance of face recognition is achievable without compromising privacy of the data owners. We evaluate our approach on three image datasets: Yale, Olivetti and Glasses datasets - the last is derived from the former two. Our approach can serve as a key enabler for real-world deployment of privacy-preserving face recognition applications, and provides a promising direction to researchers and private sectors.