Recently, adaptive beamforming methods have been successfully applied to medical ultrasound imaging, resulting in significant improvement in image quality compared to non-adaptive delay-and-sum (DAS) beamformer. Most of the adaptive beamformers presented in the ultrasound imaging literature are based on the minimum variance (MV) beamformer which can improve the imaging resolution while retaining the contrast. The main objective of this research is to present a beamformer which could improve the imaging resolution and contrast, at the same time. In this paper, we have applied the eigenspace-based MV (EIBMV) beamformer to medical ultrasound imaging and shown the simultaneous improvement in imaging resolution and contrast. EIBMV beamformer utilizes the eigenstructure of the covariance matrix to enhance the performance of the MV beamformer. The weight vector of the EIBMV is found by projecting the obtained MV weight vector onto a vector subspace constructed from the eigenstructure of the covariance matrix. EIBMV beamformer shows a significant reduction in the sidelobe levels while representing the same mainlobe width as the MV. Specifically, in the point targets phantom, the proposed method decreases the sidelobes about 22 dB and 29 dB compared to MV and DAS, respectively. Furthermore, the proposed method increases the contrast of simulated cyst phantom about 8.6 dB and 14.1 dB and also improves the contrast-to-noise ratio about 31% and 61%, compared to MV and DAS, respectively.