This article investigates the use of a dual-slope delta modulation (DSDM) technique to control a dynamic voltage restorer (DVR) that can mitigate the voltage sag problems in power systems. Traditionally, the DVR uses a pulsewidth modulation technique to control the power electronic switches in a voltage source inverter (VSI). However, the VSI suffers from several disadvantages, such as ripples in the output voltage, high dv/dt, and high total harmonic distortion. To overcome these problems, this article proposes a novel DSDM technique for a current source inverter (CSI) based DVR. The proposed DSDM technique generates the switching pulses for the power electronic switches in the CSI to produce the required missing voltage waveforms with the necessary phase angle jump to restore the load voltage to its nominal value following power systems faults. The DVR usually requires an energy storage device to support the system voltage during voltage sag, which is referred to as a storage-energy-supplied (SES) DVR. However, the energy storage device makes the DVR bulkier and costlier. A line-energy-supplied (LES) DVR scheme has been proposed in the literature that can eliminate the need for the energy storage device and hence has the potential to reduce the cost of the DVR. To validate the proposed DSDM technique, different types of fault-induced voltage sags are simulated in a radial distribution system. The proposed DSDM technique is tested to control the CSI-based SES-DVR and LES-DVR to mitigate the voltage sag. The simulation results show that the proposed DSDM technique is effective to mitigate the voltage sags by accurately injecting the required missing voltage both in magnitude and phase angle.