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This paper presents a fast global motion estimation (GME) algorithm based on gradient methods (GM), which can be used for real-time applications, such as MPEG4 video compression. This approach improves the existing state-of-the-art GME algorithms by introducing two major modifications: first, only a small subset (down to 3%) of the original image pixels is used in the estimation process. Second, a warp-free formulation of the basic GM is derived, further decreasing the computational complexity. Experimental results show no loss of GME accuracy and compression efficiency compared to the MPEG-4 verification model, while reducing the computation complexity of the GME by a factor of 20.