In functional brain images obtained by analyzing higher human brain functions using functional magnetic resonance imaging (fMRI), one serious problem is that these images depict false activation areas (artifacts) resulting from image-to-image physiological movements of subject during fMRI data acquisition. In order to truly detect functional activation areas, it is necessary to eliminate the effects of physiological movements of subject (i.e., gross head motion, pulsatile blood and cerebrospinal fluid (CSF) flow) from fMRI time series data. In this paper, we propose a method for eliminating artifacts due to not only rigid-body motion such as gross head motion, but also non-rigid-body motion like the deformation caused by the pulsatile blood and CSF flow. The proposed method estimates subject movements by using gradient methods which can detect subpixel optical flow. Our method estimates the subject movements on a "pixel-by-pixel" basis, and achieves the accurate estimation of both rigid-body and non-rigid-body motion. The artifacts are reduced by correction based on the estimated movements. Therefore, brain activation areas are accurately detected in functional brain images. We demonstrate that our method is valid by applying it to real fMRI data and that it can improve the detection of brain activation areas.