A support arm with a multiple degree of freedom locking device includes a support arm unit, an outer housing unit, a feed screw, a conical push block, and two conical baffles. When the feed screw rotates in a first direction, the conical push block and the conical baffle are driven are rotated to make the outer annular baffle slanting surface press against the inner surface of the pivot space and the first and second pivot portions, so that the lateral housing is unable to pivot with respect to the upper and lower housing, and the first and second pivot portions are positioned between the two ears in a non-rotatable manner, when the feed screw rotates reversely, the lateral housing will be able to pivot with respect to the upper and lower housing, and the first and second pivot portions are able to pivot with respect to the two ears.