Vortex beams have application potential in multiplexing communication because of their orthogonal orbital angular momentum (OAM) modes. OAM add-drop multiplexing remains a challenge owing to the lack of mode selective coupling and separation technologies. We proposed an OAM add-drop multiplexer (OADM) using an optical diffractive deep neural network (ODNN). By exploiting the effective data-fitting capability of deep neural networks and the complex light-field manipulation ability of multilayer diffraction screens, we constructed a five-layer ODNN to manipulate the spatial location of vortex beams, which can selectively couple and separate OAM modes. Both the diffraction efficiency and mode purity exceeded 95% in simulations and four OAM channels carrying 16-quadrature-amplitude-modulation signals were successfully downloaded and uploaded with optical signal-to-noise ratio penalties of ∼1 dB at a bit error rate of 3.8 × 10-3. This method can break through the constraints of conventional OADM, such as single function and poor flexibility, which may create new opportunities for OAM multiplexing and all-optical interconnection.