Robotic wire-feed additive manufacturing technology is possible to directly fabricate metallic overhangs without support structures through multi-direction deposition. To automatically produce complex components with overhangs, an efficient multi-direction slicing algorithm to slice CAD models into a set of proper layers is required. This paper reports the concept and implementation of a new strategy for multi-direction slicing of CAD models represented in STL format. An input STL model is firstly decomposed into sub-volumes using a simple curvature-based volume decomposition method. Accordingly, each sub-volume is able to be built in a single direction. Then a depth-tree structure is introduced to regroup the decomposed sub-volumes and provide the slicing sequences. Consequently, sub-volumes are separately sliced along their associated appropriate build directions in sequence. The proposed multi-direction slicing strategy is shown to be simple and efficient for STL models with sharp edges.