In order to estimate the covariance matrix structure of compound-Gaussian clutter, a Fast converging estimator (FCE) is proposed. Moreover, for the match case, the FCE is independent of the clutter power levels. Furthermore, the simulation results show that the estimation accuracy of FCE improves as the one-lag correlation coefficient or the number of secondary data increases, but it is degraded as the number of pulses increases. In addition, the FCE is very robust with respect to different subsets. Compared to the existing estimators, the FCE accelerates convergence rate and improves estimation accuracy with moderate computational burden.