Methods and apparatus of processing 360-degree virtual reality (VR360) pictures are disclosed. According to one method, if a leaf coding unit contains one or more face edges, the leaf processing unit is split into sub-processing units along the face edges without the need to signal the partition. In another method, if the quadtree (QT) of binary tree (BT) partition depth for a processing unit has not reached the maximum QT or BT depth, the processing unit is split. If the processing unit contains a horizontal face edge, QT or horizontal BT partition is applied. If the processing unit contains a vertical face edge, QT or vertical BT partition is applied.