A 3-dimensional (3D) variable-axis machine is disclosed, which includes a frame spaced from a base to be disposed at an upper surface of a workpiece, a pair of forward and backward pivoting frames having an arch shape connected to the frame, a pair of leftward and rightward pivoting frames having an arch shape and a relatively less height than the forward and backward pivoting frames to be connected across the forward and backward pivoting frames, and a spindle vertically inserted in an intersectional portion between the forward and backward and the leftward and rightward pivoting frames to be pivoted corresponding to movements of the both pivoting frames. The spindle is connected to a sliding member, and the sliding member is connected to a lower surface of the forward and backward pivoting frames and an upper surface of the leftward and rightward pivoting frames in a sliding manner.