In this paper, an adaptive block coding order for intra prediction is proposed. Modern video coding standards, including the most recent High Efficiency Video Coding (HEVC), utilize fixed scan orders in processing blocks during intra coding. However, the fixed scan orders typically result in residual blocks with noticeable edge patterns. That means the fixed scan orders cannot fully exploit the content-adaptive spatial correlations between adjacent blocks, thus the bitrate after compression tends to be large. To reduce the bitrate induced by inaccurate intra prediction, the proposed approach adaptively chooses both the block and subblock coding orders by minimizing the coding cost. Specifically, determining the block coding order is formulated as a traveling salesman problem that is solved using dynamic programming. Besides the block coding order, we also design the subblock coding order in each block with an adaptive manner. The experimental results demonstrate a Bjontegaard-Delta-rate reduction of up to 4.4% compared with HEVC anchor.