Ground clutter represents a significant challenge in Doppler weather radar systems, often masking weather signals and biasing the estimation of meteorological parameters. The Gaussian Model Adaptive Processing in Time Domain (GMAP-TD) algorithm offers a robust solution for clutter mitigation but suffers from high computational burden. In this paper, we introduce a novel implementation of GMAP-TD, termed GMAP-TD-FC (Fast Computation GMAP-TD), which retains the original algorithm’s effectiveness while significantly reducing computation time. Our approach employs the diagonalization of the clutter autocorrelation matrix, enabling the precomputation of filter components and reducing the computational complexity. Simulation results show that the accuracy of the proposed algorithm remains as good as that of GMAP-TD while improving the processing speed, making it well-suited for real-time radar operations.