Greyhounds are such gentle, well behaved dogs that it's easy to be lulled into a false sense of security when out walking. Normally your Grey will amble along at your side without pulling and content to be out enjoying a quiet stroll, but don't become too complacent. Though you may not be aware of it your sight hound is constantly searching the horizon and he can see far better than you. If he suddenly spots a cat 75 yards away he will lunge forward with amazing power to try to get to it. You will probably not even have seen the cat (or squirrel or other small animal) but your Greyhound certainly has. If you are holding his lead in the normal way with the loop in your hand he will probably snatch it clean out of your grip.
The safest way to hold the lead is shown in the photos below. Pass your hand through the loop of the lead and pull it down tightly against the back of your hand. Now you can hold the lead comfortably in your hand and if your dog lunges forward the loop of the lead will tighten on your hand and not be pulled out of your grip. Please remember, Greyhounds are remarkably strong dogs and their instinct to chase small animals is very powerfull. This is not their fault but the result of the training they will have undergone when they were being prepared for the race track. Don't risk loosing your best friend, he is depending on you to keep him safe.