As traditional Adaptive Direction Lifting based-Discrete Wavelet Transform(ADL-DWT) has higher computational complexity in the compression of high-resolution remote sensing images, this paper proposes a new lifting wavelet transform scheme based on Direction Prediction called DP-LWT to implement the fast and efficient compression of high-resolution remote sensing images. The new algorithm first divides a high-resolution remote sensing image into a number of non-overlapping sub-blocks. Then, the gradient operator is used to predict the best lifting direction of every sub-block in the remote sensing image quickly, and completes the direction lifting wavelet transform by the interpolation along the best lifting direction. Finally, the remote sensing image is coded by Set Partitioned in Hierarchical Tree(SPIHT). The experimental results show that the new algorithm effectively weakens the high-frequency coefficients on the non-horizontal and non-vertical directions of every image subband. Compared with the traditional ADL, the DP-LWT can effectively reduce the time computational complexity of directional prediction in lifting wavelet transform, and keeps the Peak Signal to Noise Ratio (PSNR) of the reconstructed high-resolution remote sensing image to be the same as that of the ADL basically.