If it is a manual transmission, then push the accelerator pedal down more when you release the clutch.
If it is an automatic transmission, then you probably need to get the transmission serviced. If you think the transmission isn't the problem, then get your engine serviced. To tell which is the problem, put the car in neutral and let it idle. If it is idling on low RPMs (less than 600 for gasoline, 800 for diesel [varies with car engines and age]) then it is the engine. If it bogs down when you take off from a dead stop, then it would probably be the transmission.
When a car bogs down, it puts quite a bit of unnecessary wear and tear on the engine, leading to more expensive payments. I would take your car into a mechanic shop and have them look at it.
Replace air and fuel filters.
Its broke - get a new car
There are several reasons why a car will start and then bog down when the accelerator is pushed. Some of the reasons could be plugs, fuel pump, or the catalytic converter.
It does not always mean that will happen, but it is certainly a common cause and if your car is sputtering and bogs down it would be one of the first things to check.
maby your acclator pump is not working you might have a vaccume leak your carb may be to big for the motor
newer cars could be air filter or fuel filter. older cars could also have improper timing on the plugs.
check to make sure the distributor cap is not cracked. check the spark plug wires are no arcing off metal or each other. just make sure they are not touching anything - if they are, use a spray bottle with water and spray it over the plug wires while the car is running. if you see little sparks and your car bogs then the plug wires are the problem.
In a cold engine, the fuel that is introduced to the air to create the fuel air mixture sometimes does not fully evaporate, resulting in incomplete combution, which in turn reduces power.
put gas in it!
It could be not getting enough air, if the filter is pushed too far down on the pipe, it would cause it to do that.
Have you checked your exhaust system, your catalytic converter may be pluged.
Maybe your alternator is on its final leg.
could be the air-conditioning. I had that and it was minor to fix.