Block-design is a popular experimental paradigm for functional near-infrared spectroscopy (fNIRS). Traditional block-design analysis techniques such as generalized linear modeling (GLM) and waveform averaging (WA) assume that the brain is a time-invariant system. This is a flawed assumption. In this paper, we propose a parametric Gaussian model to quantify the time-variant behavior found across consecutive trials of block-design fNIRS experiments. Using simulated data at different signal-to-noise ratios (SNRs), we demonstrate that our proposed technique is capable of characterizing Gaussian-like fNIRS signal features with ≥3dB SNR. When used to fit recorded data from an auditory block-design experiment, model parameter values quantitatively revealed statistically significant changes in fNIRS responses across trials, consistent with visual inspection of data from individual trials. Our results suggest that our model effectively captures trial-to-trial differences in response, which enables researchers to study time-variant brain responses using block-design fNIRS experiments.