Differential privacy is a strong, cryptographically-motivated definition of privacy that has recently received a significant amount of research attention for its robustness to known attacks. The principal component analysis (PCA) algorithm is frequently used in signal processing, machine learning and statistics pipelines. In this paper, we propose a new algorithm for differentially-private computation of PCA and compare the performance empirically with some recent state-of-the-art algorithms on different data sets. We intend to investigate the performance of these algorithms with varying privacy parameters and database parameters. We show that our proposed algorithm, despite guaranteeing stricter privacy, provides very good utility for different data sets.