Likely it's just the tension on the sear spring is too light. If someone has altered the sear or hammer by stoning it, you may need a new hammer and/or sear. If its the spring, it can be fixed easily by bending the left finger forward. This is a very common problem when someone does a trigger job and tries to get the pull too light. Has the gun had a trigger job? What model? Series 70 or 80?
This is a potentially dangerous situation. I would not fire the gun again until it is fixed. It could easily go "full auto".