Mental state monitoring is a hot topic especially in neurorehabilitation, skill training, etc, for which the functional near-infrared spectroscopy (fNIRS) has been suggested to be used, and fewer detection channels and cross-subject performance are usually required for real-world application. To this goal, we propose a transformer-based method for cross-subject mental workload classification using fewer channels of fNIRS. Firstly, the input fNIRS signals in a window are divided into patches in the temporal order and transformed into embeddings, to which a classification token and learnable position embeddings are added. Then, a transformer encoder is used to learn the long-range dependencies among the embeddings, of which the output classification token is sent to a multilayer perceptron (MLP) head. Mental workload classification results can be represented by the outputs of the MLP head. Finally, comparison experiments were conducted on the open-access fNIRS2MW dataset. The results show that, the proposed method can outperform previous methods in cross-subject classification accuracy, and relatively efficient computation can be obtained.