A car sputtering when accelerating can be caused by several different things.
Things such as clogged fuel injectors, clogged fuel filter, low fuel pressure, bad fuel pump, bad spark plugs, bad ignition wires, bad ignition coils etc.
I would first check to make sure the engine is getting enough fuel and have the fuel injectors cleaned or put some fuel injector cleaner in your gas tank and see if the problem goes away.
If that's not it then your fuel filter could be clogged or the fuel injectors could be plugged up too bad and need cleaning or the fuel injectors could be faulty.
Then if that's not the problem your fuel pump could be going bad and causing low fuel pressure.
Take the vehicle to a mechanic if possible and let them know that the car sputters when it accelerates and they can usually tell pretty quickly what the exact cause is.