Electrowetting-on-dielectric digital microfluidics (EWOD DMF) has recently emerged as a promising technology for a variety of applications based on the manipulation of discrete microdroplets. A great deal of effort has been devoted to advancing this technology by means of enhancing droplet speed and stability. In this work, we numerically investigate the continuous droplet transport process in a parallel-plate EWOD DMF device with a previously proposed "stripped electrode" design and compare it with the transport motion of the conventional "square electrode" design. The microfluidic droplet motion is solved by a finite volume formulation on a fixed computational domain. The gas-liquid interface of a droplet is captured by a coupled level-set and volume-of-fluid scheme with the surface tension force at the interface computed by the continuum surface force method. A simplified viscous stress scheme reliant on the Hele-Shaw flow model is used to evaluate the viscous forces exerted by the parallel plates. The numerically simulated transport processes of the "stripped electrode" and "square electrode" designs show good agreement with the experimental results. Furthermore, a parametric study is conducted in which the influences of the strip number, activated contact angle, and gap spacing between the plates on droplet transport speed and stability are examined. It has been found that both the transport speed and stability can be noticeably improved by the "stripped electrode" design, which can be adopted for promoting the transport efficiency in a large number of droplet-based applications utilizing parallel-plate EWOD DMF systems.