A storage device carrier includes a first frame and a second frame. The first frame includes two opposite sidewalls. Two through holes are defined in each of the sidewalls, for allowing screws to extend there through. The second frame is detachably mounted in the first frame. The second frame includes two opposite side plates. Each side plate defines two through slots for allowing screws and unthreaded fasteners to extend there through. When the second frame is mounted in the first frame, the side plates of the second frame respectively abut against the sidewalls of the first frame, and the through slots of the side plates align with the through holes of the sidewalls respectively. A mounting apparatus having the storage device is also provided.