The near-field effect of short-range multiple-input multiple-output (MIMO) systems imposes many challenges on direction-of-arrival (DoA) estimation. Most conventional scenarios assume that the far-field planar wavefronts hold. In this paper, we investigate the DoA estimation problem in short-range MIMO communications, where the effect of near-field spherical wave is non-negligible. By converting it into a regression task, a novel DoA estimation framework based on complex-valued deep learning (CVDL) is proposed for the near-field region in short-range MIMO communication systems. Under the assumption of a spherical wave model, the array steering vector is determined by both the distance and the direction. However, solving this regression task containing a massive number of variables is challenging, since datasets need to capture numerous complicated feature representations. To overcome this, a virtual covariance matrix (VCM) based on received signals is constructed, and thus such features extracted from the VCM can deal with the complicated coupling relationship between the direction and the distance. Although the emergence of wireless big data driven by future communication networks promotes deep learning-based wireless signal processing, the learning algorithms of complex-valued signals are still ongoing. This paper proposes a one-dimensional (1-D) residual network that can directly tackle complex-valued features due to the inherent 1-D structure of signal subspace vectors. In addition, we put forth a cropped VCM based policy which can be applied to different antenna sizes. The proposed method is able to fully exploit the complex-valued information. Our simulation results demonstrate the superiority of the proposed CVDL approach over the baseline schemes in terms of the accuracy of DoA estimation.