Might be carbon build-up in the combustion chambers causing after-run. Run some combustion chamber cleaner to help clean up the carbon. You can also slowly pour a large glass of water down the intake while rev'ing the engine (find someone who has done this and knows what they are doing) to clean out the carbon buildup.
Some carbs have a solenoid that allows the throttle to snap shut when the ignition is turned off to prevent the after-run. Does yours?
Probably best to start with a good overall tune-up, making sure that the ignition system (plugs, wires, cap, rotor, points/condensor, dwell, timing, if equiped) are in good shape. Then clean carburetor, replace filters, check for vacuum leaks, cracked vacuum lines, etc., and adjust the carburetor per the shop manual.
Good luck!
I sure do miss adjusting carburetors and changing points (at times)!