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For adaptive ultrasound imaging, accurate estimation of the covariance matrix is of great importance, and it has a fundamental influence on the performance of the adaptive beamformer. In this paper, a new forward-backward generalized sidelobe canceler (FBGSC) approach is proposed for medical ultrasound imaging, which uses forward and backward subaperture averaging to accurate estimate the covariance matrix. And resulted from accurate estimating of covariance matrix, FBGSC can achieve better lateral resolution and contrast without preprocessing algorithms. Field II is applied to obtain the simulated echo data of scattering points and a circular cyst. Beamforming responses of scattering points show that FBGSC can improve the lateral resolution by 55.7% and 66.6% compared with synthetic aperture (SA) and delay-and-sum (DS), respectively. Similarly, the simulated results of circular cyst show that FBGSC can obtain better beamforming responses than traditional adaptive beamformers. Finally, an experiment is conducted based on the real echo data of a medical ultrasound system. Results demonstrate that the FBGSC can improve the imaging quality of medical ultrasound imaging system, with lower computational demand and higher reliability.