Abstract: The controllability of delay degenerate differential control systems is discussed. Firstly, delay degenerate differential control system was transformed to be canonical form, and the connected terms were gotten rid of, had delay degenerate differential control systems with independent subsystems. For the general delay degenerate differnetial control systems, it was gotten that the necessary and sufficient condition of that they are controllable is that their reachable set is equal to the whole space. For the delay degenerate differential control systems with independent subsystems, it was gotten that the necessary and sufficient conditions of that they are controllable are that their reachable sets are equal to their corresponding subspaces. Then some algebra criteria were gotten. Finally, an example was given to illustrate the main results.