A firearm magazine loader (30) comprises a body (32) coupled to a movable press (40), a plunger (20) extending out of the press towards the body, and a magazine aligner (52). The body is hollow and adapted to fit and slide over an open side of a magazine (10). A spring (48) is positioned between the body and the press to force them apart. To load the magazine, the user squeezes the press towards the body such that plunger is over a topmost round (12) in the magazine, and then presses down the loader, causing the plunger to force the topmost round further into the magazine to form a vacant space below lips (14) of the magazine. This enables a new round (13) to be rearwardly, case first, loaded inside the vacant space. The user then eases the down force on the loader allowing the spring (16) of the magazine to force up all the rounds in the magazine towards the lips while releasing the press for allowing the spring of the press to force the press and plunger back to their original position. The magazine aligner is positioned inside the body for centering the open side of magazines of different widths and depth mounted in the loader in line with the plunger.