An increasing number of functional near-infrared spectroscopy (fNIRS) studies utilize a general linear model (GLM) approach, which serves as a standard statistical method for functional magnetic resonance imaging (fMRI) data analysis. While fMRI solely measures the blood oxygen level dependent (BOLD) signal, fNIRS measures the changes of oxy-hemoglobin (oxy-Hb) and deoxy-hemoglobin (deoxy-Hb) signals at a temporal resolution severalfold higher. This suggests the necessity of adjusting the temporal parameters of a GLM for fNIRS signals. Thus, we devised a GLM-based method utilizing an adaptive hemodynamic response function (HRF). We sought the optimum temporal parameters to best explain the observed time series data during verbal fluency and naming tasks. The peak delay of the HRF was systematically changed to achieve the best-fit model for the observed oxy- and deoxy-Hb time series data. The optimized peak delay showed different values for each Hb signal and task. When the optimized peak delays were adopted, the deoxy-Hb data yielded comparable activations with similar statistical power and spatial patterns to oxy-Hb data. The adaptive HRF method could suitably explain the behaviors of both Hb parameters during tasks with the different cognitive loads during a time course, and thus would serve as an objective method to fully utilize the temporal structures of all fNIRS data.