One of the few titles that should be capitalised. Avoid abbreviating to DG.

The hyphen is important. Here's an example from a photo caption that shows why: 

Stephen Hawking (left) with CERN Director General Rolf Heuer. 

The sentence above could be (incorrectly) interpreted to mean that Rolf Heuer is a (military) General, and he is also Director of CERN. 

The hyphen renders the compound adjective unambiguous, Heuer is a Director-General.

The plural of Director-General is Directors-General.