A novel laser self-mixing interferometry vibration measurement algorithm based on the local maximum detection technique is proposed, that can reconstruct micro vibrations rapidly and easily. In this article, the principles of the local maximum detection algorithm are analyzed in detail, and the process of solving the window function is emphasized. The major advantage of the method is that it does not involve any complicated calculations and removes the need for optical/electromechanical components. The validity of the presented method is confirmed by means of simulated signals and demonstrated via several experiments for harmonic and aleatory motion.