Functional near-infrared spectroscopy (fNIRS) is a brain imaging method introduced relatively recently, which is promising to implement brain-computer interfaces. However, there is still a lack of research on fNIRS signal classification, particularly that focusing on improved machine learning techniques for non-motor tasks. In this paper, we propose a novel deep learning method using brain connectivity for resting-state fNIRS signal classification. Our method is based on the powerful modeling capability of the convolutional neural network that learns the brain connectivity patterns residing in the fNIRS signal. In particular, we present a new data augmentation method that can overcome the scarcity of fNIRS data. Experimental results of subject-independent classification of flourishing levels demonstrate the superiority of our approach to conventional approaches. It is also shown that the data augmentation strategy is effective for improving classification performance.