The cause of a cars sputtering when accelerating is either due to low fuel pressure or your fuel injectors are dirty not allowing the correct amount of fuel pressure and fuel spray to get into your intake to fire the cylinders properly.
I would add some fuel injector cleaner to your gasoline tank and then let the car idle for a few minutes and then drive slowly around town and then get out on the highway and see if the fuel injectors clear up and the engine sputtering stops.
If the engine is still sputtering then you might need a professional fuel injector cleaning done to clean the fuel injectors.
Or you could have bad fuel injectors or your fuel pump is going bad and not putting out the correct fuel pressure.
You can have a mechanic check your fuel pressure to see if your fuel pump is working properly or even get your fuel injectors cleaned up or checked out.