In this paper, we present the first evidence that perceived speech can be identified from the listeners' brain signals measured via functional-near infrared spectroscopy (fNIRS)—a non-invasive, portable, and wearable neuroimaging technique suitable for ecologically valid settings. In this study, participants listened audio clips containing English stories while prefrontal and parietal cortices were monitored with fNIRS. Machine learning was applied to train predictive models using fNIRS data from a subject pool to predict which part of a story was listened by a new subject not in the pool based on the brain's hemodynamic response as measured by fNIRS. fNIRS signals can vary considerably from subject to subject due to the different head size, head shape, and spatial locations of brain functional regions. To overcome this difficulty, a generalized canonical correlation analysis (GCCA) was adopted to extract latent variables that are shared among the listeners before applying principal component analysis (PCA) for dimension reduction and applying logistic regression for classification. A 74.7% average accuracy has been achieved for differentiating between two 50 s. long story segments and a 43.6% average accuracy has been achieved for differentiating four 25 s. long story segments. These results suggest the potential of an fNIRS based-approach for building a speech decoding brain-computer-interface for developing a new type of neural prosthetic system.