Classification of olfactory-induced electroencephalogram (EEG) signals has shown great potential in many fields. Since different frequency bands within the EEG signals contain different information, extracting specific frequency bands for classification performance is important. Moreover, due to the large inter-subject variability of the EEG signals, extracting frequency bands with subject-specific information rather than general information is crucial. Considering these, the focus of this letter is to classify the olfactory EEG signals by exploiting the spectral-domain information of specific frequency bands. In this letter, we present an olfactory EEG signal classification network based on frequency band feature extraction. A frequency band generator is first designed to extract frequency bands via the sliding window technique. Then, a frequency band attention mechanism is proposed to optimize frequency bands for a specific subject adaptively. Last, a convolutional neural network (CNN) is constructed to extract the spatio-spectral information and predict the EEG category. Comparison experiment results reveal that the proposed method outperforms a series of baseline methods in terms of both classification quality and inter-subject robustness. Ablation experiment results demonstrate the effectiveness of each component of the proposed method.