Depth map up-sampling methods have achieved remarkable improvement by exploiting sensor fusion techniques where they assume that the depth map discontinuities and image edges coincide, and the depth values of the temporal neighbors are stable during time variation. However, inherent noise of depth data acquired by active range sensors often violates these assumptions, and results in undesirable error propagation. To alleviate the error propagation, this letter presents a new adaptive supporting method of spatially-temporally neighboring samples. On the basis of a spatial-temporal Markov random field model, the weight coefficients of the smoothness terms are adaptively computed according to the reliability of neighboring samples. The experiments show that the proposed method outperforms the previous works in terms of quantitative and qualitative criteria.