In the compound-Gaussian background, for the problem that a fusion-based detector was not fully adaptive when using the sample covariance matrix (SCM) estimation, this paper replaces SCM with the normalized sample covariance matrix (NSCM) to estimate the clutter covariance matrix and a new empirical formula of the adjustable parameter of the adaptive NSCM-based detector is derived. At last, the CFAR characteristics and detection performance of the detectors based on NSCM estimation and SCM estimation are analyzed. The results show that the adaptive NSCM-based detector, which is robust to the variation of normalized clutter covariance matrix and much less affected by the fluctuation of clutter power, exhibits better target detection performance than the adaptive SCM-based detector in the compound-Gaussian environment.