A triaxial driving device for electrodischarge machine tools having a three-liners-axes mechanism and an electrode tool and has a connecting mount, a first axial rotator, a base, a supporting arm, a second axial rotator, a third axial rotator and an electrode holder. The connecting mount is connected securely to the three-liners-axes mechanism. The first axial rotator is mounted in the connecting mount and has a rotating head. The base is connected securely to the rotating head of the first axial rotator and has a space. The supporting arm is rotatably mounted in the space of the base and has a connecting frame. The second axial rotator is securely connected to the base and the supporting arm and has a rotating head. The third axial rotator is connected to the supporting arm and has a rotating head. The electrode holder is connected to the third axial rotator and the electrode tool.