Give your hero an obscure and muddied past filled with mystery and trauma. All action hero movies are about overcoming unbelievable odds (with guts, determination, good instincts, and a lot of firepower) so your hero needs to have this in his blood. Did he grow up as a foster kid, in a tough neighborhood, or even more interesting, was he sent at a young age to a secret spy school somewhere in the Russia?
Make your hero resistant to corporate interests, greed and all the desires and temptations most people fall victim too. An action hero needs to be strong both physically and mentally, and this will resonate on the screen on a background of explosions and firepower.
Put your hero at odds with both the bad guys and the cops (think Die Hard). As they try to help resolve a situation, they are the only person able to stop the problem, and they have to cut through the bureaucratic red tape and politics to get the job done right.
Give them a side kick. Someone who shares a little bit of their resentment towards the establishment, but sucks it up and does his job anyway. Someone has to side with your hero, and usually this person helps in a small way doing what they can, because they believe in them for no other reason than they think they are a good guy. The audience will relate to this and feel like a part of the action.
Make him stoic and determined, even in the face of the greatest danger. Your hero is determined to get the job done, and get it done right.
Put your hero in a circumstance that tests their will and moral fortitude. Maybe they need to choose between saving a family and running off with millions in cash from a drug bust gone bad. Or, they are offered a place in crime king pin's empire to give up the fight for good. Make it interesting.