We present a new, simple method to suppress texture pattern artifacts induced by the optical heterogeneity of tissues to improve the performance of flow imaging for real-time phase-resolved optical Doppler tomography. The method performs transverse scanning of the probe beam in the forward and then reverse directions, and it takes average of the spatial phase changes between them to obtain the final velocity image. It relies on the fact that the phase changes between successive axial scans due to the optical heterogeneity of the sample are time independent, while those due to the moving particles are time dependent. We experimentally demonstrate this method by real-time imaging of a flow phantom.