trigger bounce
It could very well be trigger bounce (trigger moving rearward during recoil and tripping the sear), or a worn hammer/sear fit.
The fix could be as simple as adjusting the sear spring. (adding tension). Or you may need to have hammer and sear refit or replaced if they are damaged beyond repair.
To check for doubling or hammer bounce, With unloaded pistol and magazine drop the slide on an empty chamber a couple of times. If the hammer falls, you have a problem. Now drop the slide again this time holding the trigger forward, if the hammer stays put you have hammer bounce and need to increase pressure on th center "leg" of the sear spring.
Repeat above test, if hammer falls try increasing tension on the sear "leg" of the spring (left leg with the hook on the end).
Note: it is not recommended that you drop the slide on a empty chamber repeatedly as this can batter the sear and hammer fit. Since the pistol is doubling already, this is the easiest way to find what your problem is.
Or you can bring it to a competent 1911 smith.