In MPEG-4, global motion estimation (GME) and global motion compensation can improve the visual quality of local motion estimation/compensation. However, the computational complexity of GME is very high. Even the existing fast algorithm, FFRGMET, in the MPEG-4 OM3 software is not fast enough. In this paper, we propose a fast GME algorithm called APSGME. It uses motion vectors from the PMVFAST local motion estimation to perform early termination, foreground/background block-based segmentation, feature point selection. Experimental results shown that APSGME can achieve considerable speed-up over FFRGMET while improving the visual quality simultaneously.