For the problem of early detection of atrial fibrillation (AF) from electrocardiogram (ECG), it is difficult to capture subject-invariant discriminative features from ECG signals, due to the high variation in ECG morphology across subjects and the noise in ECG. In this paper, we propose an Discrete Biorthogonal Wavelet Transform (DBWT) Based Convolutional Neural Network (CNN) for AF detection, shortly called DBWT-AFNet. In DBWT-AFNet, rather than directly feeding ECG into CNN, DBWT is used to separate sub-signals in frequency band of heart beat from ECG, whose output is fed to CNN for AF diagnosis. Such sub-signals are better than the raw ECG for subject-invariant CNN representation learning because noisy information irrelevant to human beat has been largely filtered out. To strengthen the generalization ability of CNN to discover subject-invariant pattern in ECG, skip connection is exploited to propagate information well in neural network and channel attention is designed to adaptively highlight informative channel-wise features. Experiments show that the proposed DBWT-AFNet outperforms the state-of- the-art methods, especially for ECG segments classification across different subjects, where no data from testing subjects have been used in training.