In today’s cyber–physical microgrid systems, the consensus-based secondary control is generally utilized to settle the voltage deviation and rough current allocation issues at the primary control level. However, time delays follow inevitably the introduction of sparse communication networks, and most existing works adopt passive tolerance approaches. To actively alleviate the unavoidable delay effect in microgrids’ communication networks, a networked predictive control (NPC) strategy is proposed for an islanded DC microgrid subject to time delays in this paper. Firstly, the predictive approaches for both voltage and current are developed based on the cyber–physical microgrid model. Unlike the practice of passively tolerating time delays, the NPC strategy is proposed to actively compensate for the effect of communication delays by estimating real-time voltage and current values using the previously obtained prediction models. Moreover, to prove the generality of the developed method, the microgrid systems’ stability can be derived from the Schur stability of the closed-loop system, thus the DC microgrid can achieve voltage regulation and proportional current sharing simultaneously. Finally, the performance of our method against the time delay effect is validated by extensive experiments on an islanded 48-V DC microgrid system, in terms of its feasibility, delay tolerance ability, and robustness to load changes and communication faults. Experimental results demonstrate the effectiveness and superiority of the NPC strategy.