Presence of bias (in datasets or tasks) is inarguably one of the most critical challenges in machine learning applications that has alluded to pivotal debates in recent years. Such challenges range from spurious associations between variables in medical studies to the bias of race in gender or face recognition systems. Controlling for all types of biases in the dataset curation stage is cumbersome and sometimes impossible. The alternative is to use the available data and build models incorporating fair representation learning. In this paper, we propose such a model based on adversarial training with two competing objectives to learn features that have (1) maximum discriminative power with respect to the task and (2) minimal statistical mean dependence with the protected (bias) variable(s). Our approach does so by incorporating a new adversarial loss function that encourages a vanished correlation between the bias and the learned features. We apply our method to synthetic data, medical images (containing task bias), and a dataset for gender classification (containing dataset bias). Our results show that the learned features by our method not only result in superior prediction performance but also are unbiased.