RPM doesn't drop as I accelerate - not shifting?

I drive a 2001 Chevy Malibu. Every now and then when I take my foot off the accelerator the engine keeps going. The pedal releases but the car won't slow down. It keeps going as if the cruise control is on but it's not. When I do take my foot off the accelerator the rpm picks up a little but the car remains at the same speed. Sometimes when I press the brake pedal it will stop and sometimes it won't. Also when it happens I have to ride the brake until the car stops moving and I turn the car off and crank it once again everything is back to normal.

What could the problem be?

No the check engine light doesn't come on when it happens.

Thanks a lot! I'll have that done this weekend and see what happens. I hope this works.

Transmission problem
1999 Chevy Malibu 4 cyl Automatic 157000 miles

I was going down the road doing 55mph and then when we got to a hill the car not to want to go up the hill. The rpm was going up tp 4 and 5. And like when im in town the car will do good a 20mph but the up the rpm will go up past 2 and want go down the stay up like it want shift.

I would have the transmission checked, if the car is struggling to get up hill and reving high, could be that a gear is slipping.

Idle is way to high, at rpm 2000, after putting car in drive then back in park it raises to 3000 rpm. Happened after car was driven off road into ditch of water. We tried un hooking battery to reset the computer but no luck. What would you suggest?

I have a 2001 Chevy Malibu. Sometimes when I but the car in park the RPM's sill shoot up 2-3. Also when I have the car in drive and I havent even pushed the gas the car will continuosly accelerate. Up maybe 40 MPH. What my the problems be?

Sounds like the throttle may be sticking or a vacuum leak. A good technician with a scanner could pinpoint the problem, but that entails taking the car to a shop. Might listen under the hood and see if you can hear a whooshing noise that a vacuum leak makes. While under there, check the throttle. You can move it with your hand. Thinking more on this, its possible the idle air control valve isnt working properly, but as I said earlier, a scanner would tell that.