If you believe in astrology, a system of personality typing based on your birth date, people born under the sign of Leo have certain personality traits. This means they get upset for different reasons and express their feelings in different ways than people born under other signs. This means that dealing with an upset person born under the sign of Leo is different than dealing with someone born under a different star sign.
Tell him that you love and admire him, even though he is being difficult at this moment. Leos tend to be a little self-obsessed, so you need to make it clear to him that while his behavior is frustrating, you still feel a lot of love and respect for him as a person. This will make him easier to deal with.
Avoid criticizing him, and if you do, make it clear that you're criticizing his behavior, not him as a person. Again, Leos tend to be self-obsessed, and they take criticism personally. This doesn't mean you should accept his behavior, but you should phrase your sentences in a way that makes it clear that you are addressing the behavior, not him.
Avoid dropping hints. Leos are not creatures of subtlety; they prefer to deal with people directly, and if you are passive-aggressive or overly-subtle, your Leo friend will either not get your meaning or will choose to ignore it.
Avoid telling him what to do. Leos like to be in charge, so you should avoid undermining his perceived authority by taking it over from him. Rather, you should make suggestions in order to make him feel involved in -- even leading -- the decision-making process.
Let him lose his temper. Leos sometimes yell and scream or otherwise act out. They are quick to recover after this, but they do need to get it off their chests. Indeed, if he yells at you he will likely -- and should -- apologize to you soon after. You don't need to be a doormat, but you should bear in mind that Leos need to let their emotional energy out from time to time.