Phase retrieval with unidirectional differential phase-contrast image requires integration with noisy data, which is an illposed inverse problem. Conventional direct integration method would result in severe streak artifacts. Total variation (TV) regularization-based method would reduce the streak artifacts, but the edges parallel with phase-contrast sensitivity direction are likely to be over smoothed. We propose an improved weighted TV regularization phase retrieval method by introducing a weighting factor to the conventional TV term. When applied to simulation and experimental data, this method shows an advantage of preserving the sharpness of the edges while preserving the ability of reducing streak artifacts compared with conventional TV-regularization method.