Would you end this game with a draw or can white win?

Hi everyone, 

just recently started playing chess again after years and me and my friend were facing the following situation (white to move next). Please see screenshot: 

How would you proceed?

Can white still win the game (black obviously not)?

Black ended up putting white on check for a while. 

Yes, 1.Qf3+-. Black can't check eternally.

Note e.g. 1...Qc2+ 2.Kg3 Qc7+ 3.Qf4+ with a forced Queen trade.

Thanks Sred!

Sorry how do you read the abbreviations? So white would move Queen to which position? 

and how does the forced Queen trade work?

That's not what Black would likely play, just an example how to utilize a tactical resource often available in Queen endgames. In the long run Black will still have many checks, but White can activate the King and push the b pawn.

Try to get your king to a rank adjacent to the opponent's king so that you do what @Sred said (Although in this case the black king and pawn are placed quite badly)