I am jealous of him/ his playing

[Vladv1]

"I am jealous of him/ his playing games instead of doing his homework".
Which pronoun is correct?
Can I use a noun? Example; "I am jealous the kids playing games instead of doing their homework". The examples are mine.

 

[Tarheel]

Perhaps:

I'm jealous of him. He gets away with playing games instead of doing his homework.

 

[Piscean]

Which pronoun is correct?

You'll find some people argue for one and some for the other. Use the one you prefer.

 

[Skrej]

"I am jealous of him/ his playing games instead of doing his homework".
Which pronoun is correct?

'His' is a possessive adjective in your example, not a pronoun.

Can I use a noun? Example; "I am jealous of the kids playing games instead of doing their homework".

With the noted fix, your example would be okay.