Deep learning models were frequently reported to learn from shortcuts like dataset biases. As deep learning is playing an increasingly important role in the modern healthcare system, it is of great need to combat shortcut learning in medical data as well as develop unbiased and trustworthy models. In this paper, we study the problem of developing debiased chest X-ray diagnosis models from the biased training data without knowing exactly the bias labels. We start with the observations that the imbalance of bias distribution is one of the key reasons causing shortcut learning, and the dataset biases are preferred by the model if they were easier to be learned than the intended features. Based on these observations, we propose a novel algorithm, pseudo bias-balanced learning, which first captures and predicts per-sample bias labels via generalized cross entropy loss and then trains a debiased model using pseudo bias labels and bias-balanced softmax function. To our best knowledge, we are pioneered in tackling dataset biases in medical images without explicit labeling on the bias attributes. We constructed several chest X-ray datasets with various dataset bias situations and demonstrated with extensive experiments that our proposed method achieved consistent improvements over other state-of-the-art approaches.