A firearm firing mechanism is so configured that a hammer is retaining by a front retaining block before pressing a trigger; pressing the trigger slightly at a first stage causes a main bar to bias a rear retaining block and the front retaining block backwardly at a relatively smaller angle to release the hammer in performing a single-shot action; pressing the trigger heavily at a second stage causes the main bar at a relatively longer distance so that the hammer is kept away from the front retaining block when it is returned, and the hammer is secured by the rear retaining block upon a backward displacement of a bolt and backward biasing of the hammer, and a linkage is forced to move the rear retaining block in releasing the hammer for firing when the bolt forward again, and a continuous multi-shot firing action is performed by means of repeating this operation. Thus, the invention enhances the operation convenience in achieving single-shot and multi-shot firing actions.