High frame rate ultrasound is an emerging technique for medical ultrasound imaging. However, spatial resolution and contrast are degraded compared to conventional beamforming using focused transmit beams. In the present study, a kind of minimum variance beamformer, namely, amplitude and phase estimation (APES) beamformer, was examined for improvement of the spatial resolution. The APES beamformer estimates the desired signal, i.e., echo from the focal point, using delay-and-sum beamforming without considering the element directivity and removes it from the spatial covariance matrix. By omitting the element directivity, the error in estimation of the desired signal increases and, as a result, more part of the desired signal remains in the spatial covariance matrix. Consequently, sub-array averaging is necessary for further suppressing the desired signal contained in the spatial covariance matrix. In the present study, the APES beamformer was modified so as to consider the element directivity in estimation of the desired signal. Also, the proposed APES beamforming was further modified to be applied to outputs of sub-aperture beamforming to reduce dimension of the spatial covariance matrix. In the present study, the effect of the element directivity on APES beamforming was evaluated by a basic experiment using a phantom. In parallel beamforming with the conventional DAS, lateral spatial resolution, which was evaluated from the lateral full width at half maximum of the amplitude profile of an echo from a fine wire, was 0.50 mm. Using conventional APES, the lateral spatial resolution was improved to 0.26 mm. Lateral spatial resolution was further improved to 0.25 mm using the modified APES. In both APES beamforming, sub-array averaging was not used, and outputs from 6 sub-apertures were processed. Also in B-mode imaging of a carotid artery, undesired echoes are suppressed significantly by the modified APES.