The delay-and-sum (DAS) beamformer is the most commonly used method in medical ultrasound imaging. Compared with the DAS beamformer, the minimum variance (MV) beamformer has an excellent ability to improve lateral resolution by minimizing the output of interference and noise power. However, it is hard to overcome the tradeoff between satisfactory lateral resolution and speckle preservation performance due to the fixed subarray length of covariance matrix estimation. In this study, a new approach for MV beamforming with adaptive spatial smoothing is developed to address this problem. In the new approach, the generalized coherence factor (GCF) is used as a local coherence detection tool to adaptively determine the subarray length for spatial smoothing, which is called adaptive spatial-smoothed MV (AMV). Furthermore, another adaptive regional weighting strategy based on the local signal-to-noise ratio (SNR) and GCF is devised for AMV to enhance the image contrast, which is called GCF regional weighted AMV (GAMV). To evaluate the performance of the proposed methods, we compare them with the standard MV by conducting the simulation, in vitro experiment, and the in vivo rat mammary tumor study. The results show that the proposed methods outperform MV in speckle preservation without an appreciable loss in lateral resolution. Moreover, GAMV offers excellent performance in image contrast. In particular, AMV can achieve maximal improvements of speckle signal-to-noise ratio (SNR) by 96.19% (simulation) and 62.82% (in vitro) compared with MV. GAMV achieves improvements of contrast-to-noise ratio by 27.16% (simulation) and 47.47% (in vitro) compared with GCF. Meanwhile, the losses in lateral resolution of AMV are 0.01 mm (simulation) and 0.17 mm (in vitro) compared with MV. Overall, this indicates that the proposed methods can effectively address the inherent limitation of the standard MV in order to improve the image quality.