Non-parametric hemodynamic response function (HRF) estimation in noisy functional near-infrared spectroscopy (fNIRS) plays an important role when investigating the temporal dynamics of a brain region response during activations. Assuming the drift Lipschitz continuous; a new algorithm for non-parametric HRF estimation from the oxygenated (HbO) and deoxygenated (HbR) fNIRS time-series is derived in this paper. The proposed algorithm estimates the HRF by applying a first order differencing to the fNIRS time series samples. It is shown that the proposed HRF estimator is root N consistent. Its performance is assessed using both simulated and a real fNIRS data set obtained from a motor activity experiment. The application results reveal that the proposed HRF estimation method is efficient both computationally and in terms of accuracy.