In order to make the dynamic voltage restorer (DVR) concurrently compensate for low-order harmonics and voltage sag, and eliminate the influence of digital control on system performance, we propose a novel double closed-loop digital control strategy, consisting of the fundamental proportional resonant (PR) control in a voltage loop and selective harmonic PR control in an inductance current loop. Then, we mainly analyse the discretization effects of the virtual LC method and the step response method, and further present a straightforward digital design method. Next, with this method, we design the parameters of the fundamental and selective harmonic PR controllers in the discrete domain, which inhibit the influence of sampling, calculation delay etc. on the steady-state error and the dynamic response performance. Finally, an 11-kVA DVR prototype is developed and tested. The experimental results indicate that the proposed control strategy satisfies the requirement of voltage quality for sensitive loads and achieves a good dynamic response performance.