Inter-user interference (IUI) mitigation has been an essential issue for multi-user multiple-input multiple-output (MU-MIMO) communications. The commonly used linear processing schemes include the maximum-ratio combining (MRC), zero-forcing (ZF) and minimum mean squared error (MMSE) beamforming, which may result in the unfavorable performance or complexity as the antenna number grows. In this paper, we introduce a low-complexity linear beamforming solution for the IUI mitigation by using the convolutional beamspace (CBS) technique. Specifically, the dimension of channel matrix can be significantly reduced via the CBS preprocessing, thanks to its beamspace and spatial filtering effects. However, existing methods of the spatial filter design mainly benefit from the Vandermonde structure of channel matrix, which only holds for the far-field scenario with the uniform plane wave (UPW) model. As the antenna size increases, this characteristic may vanish in the near-field region of the array, where the uniform spherical wave (USW) propagation becomes dominant. To gain useful insights, we first investigate the beamforming design and performance analysis of the CBS-based beamforming based on the UPW model. Our results unveil that the proposed CBS-based MMSE beamforming is able to achieve a near-optimal performance but demands remarkably lower complexity than classical ZF and MMSE schemes. Furthermore, our analysis is also extended to the near-field case. To this end, a novel optimization-based CBS approach is proposed for preserving spatial filtering effects, thus rendering the compatibility of the CBS-based beamforming. Finally, numerical results are provided to demonstrate the effectiveness of our proposed CBS-based beamforming method.