Recently, deep learning has gained great attention in decoding the neuro-physiological signal. However, which one (classical machine learning or deep learning) has better performance for decoding the functional near-infrared spectroscopy (fNIRS) signal is still lack of full verification. Thus, in this paper, we systematically compared the performance of many classical machine learning methods and deep learning methods in fNIRS data processing for decoding the mental arithmetic task. The classical machine learning methods such as decision tree, linear discriminant analysis (LDA), support vector machine (SVM), K-Nearest Neighbor (KNN) and ensemble methods with strict feature extraction and screening, were used for performance comparison, while the long short-term memory-fully convolutional network (LSTM-FCN) method as a representative of deep leaning methods was applied. Results showed that the classification performance of SVM was the best among the classical machine learning methods, achieving that the average accuracy of the subject-related/unrelated were 91.0% and 83.0%, respectively. Furthermore, the classification accuracy of deep learning was significantly better than that of the involved classical machine learning methods, where the accuracy of deep learning could reach 95.3% with subject-related condition and 97.1% with subject-unrelated condition, respectively. Thus, this paper has totally showed the excellent performance of LSTM-FCN as a representative of deep learning in decoding brain signal from fNIRS dataset, which has outperformed many classical machine learning methods.