Extensive use of low-cost handheld cameras triggers handshakes and camera gestures to the majority of captured images. Methods to eliminate undesired camera movements from Video sequences have been developed for Video Stabilization (VS). Movement of camera-related artifacts may also affect the efficiency of most 2D video stabilization processes. By improving the motion estimation or motion fluidity process, the performance of the VS procedure can be improved. This article therefore proposes a global approach for video stabilization, which combines an efficient motion smoothing algorithm with a truncating motion calculation. Smoothing up of the high-frequency movements within frames achieves the stabilization. During the first step, the global movement estimate is selecting global motion vectors with the truncated Taylor series expansion. An FIR philter is used in this article to smooth global movement vectors by estimated motion vectors to stabilize shaky images. The proposed method eliminates undesirable movements efficiently and also conserves video information. Motion smoothening eliminates the loss of frame areas after stabilization. The method's efficiency is also compared with the latest global video stability results.