Applying a deep convolutional neural network CNN to no reference image quality assessment (NR-IQA) is a challenging task due to the lack of a training database. In this paper, we propose a CNN-based NR-IQA framework that can effectively solve this problem. The proposed method–the Deep Blind image Quality Assessment predictor (DeepBQA)– adopts two-step training stages to avoid overfitting. In the first stage, a ground-truth objective error map is generated and used as a proxy training target. Then, in the second stage, the subjective score is predicted by learning a sensitivity map, which weights each pixel in the predicted objective error map. To compensate the inaccurate prediction of the objective error on the homogeneous regions, we additionally suggest a reliability map. Experiments showed that DeepBQA yields a state-of-the-art correlation with human opinions.