Atrial fibrillation (AF) is the most clinically diagnosed arrhythmia in cardiac pathology. The incidence of AF begins at a very early age and its initial state is paroxysmal atrial fibrillation (PAF). This type of heart disease can be detected and predicted by analyzing the spectrogram of a surface electrocardiogram (ECG) signal. In many studies, different ECG signal formats and convolutional neural network (CNN) architectures have been used. However, the lack of good signal preprocessing or signal adequacy may have affected the accuracy, especially on short-term ECG signals. In this study, we analyzed a preprocessed ECG signal, determined the optimal set to predict PAF, and evaluated the accuracy using ECG signals of different durations. The PAF Prediction Challenge–PhysioNet database was used to extract spectrograms in 30-sec and 5-sec windows for two classes (Normal, PAF) and 3 classes (Normal, Close-AF, Distant-AF). Then, the AlexNet architecture was used. The proposed method achieved a two-class accuracy of 99.92% with a 30-sec window and 99.42% with a 5-sec window, improving the PAF prediction performance compared with similar works. In addition, the three-class accuracies were 96.92% and 97.43% with windows of 30-sec, and 5-sec, respectively. These results prove the efficacy of the method for the early diagnosis of PAF, even based on short-term ECG signals.