In this article, we investigate the analog–digital hybrid transceiver optimization for multiple-input–multiple-output (MIMO) Internet of Things (IoT) systems, aiming at maximizing the sum rate of multiple IoT devices in downlink communications. We first derive the downlink–uplink duality for the MIMO communications with analog–digital hybrid structures. Based on this, the intractable MIMO downlink sum-rate maximization is equivalently transferred into an easier-to-handle virtual uplink counterpart. In order to solve the nonconvex virtual uplink problem effectively, we resort to decouple the involved digital and analog matrix variables. On the one hand, we propose two kinds of algorithms for the analog matrices optimizations, namely, the joint design and the separate design. Specifically, the joint design optimizes the analog precoder and equalizer matrices in an alternating manner. In each iteration, an element-wise optimization algorithm is utilized to optimize the analog matrix variables under constant modulus constraints. For the separate design, the analog precoder and equalizer matrices are optimized separately via the elaborately designed space alignments with lower computational complexities. On the other hand, the digital precoders can be computed with fixed analog matrix variables, in which a modified iterative water-filling algorithm is proposed. Finally, numerical results demonstrate the superior performance advantages of the proposed algorithms over several benchmark algorithms.