We present a modified M-estimation based method for fast global 3D point cloud registration which rapidly converges to an optimal solution while matching or exceeding the accuracy of existing global registration methods.The key idea of our work is to introduce weighted median based M-estimation for re-weighted least squares adeployed in a graduated fashion which takes into account the error distribution of the residuals to achieve rapid convergence to an optimal solution. The experimental results on synthetic and real data sets show the significantly improved convergence of our method with a comparable accuracy with respect to the state-of-the-art global registration methods.