This paper proposes a computationally efficient approach of adaptive directional wavelet transform (AD WT). The AD WT is based on lifting implementation of WT, and it is able to transform an image along diagonal orientations as well as traditional horizontal and vertical directions. The AD WT sacrifices computational speed for its good image coding performance. We present an alternative method to find the best transform directions by pre-directional filterings for the AD WT. The proposed direction calculation method shows very comparable image coding performance to the conventional one, whereas its computational cost is relatively very low.