Electroadhesion is a versatile and controllable adhesion mechanism that has been used extensively in robotics. Soft electroadhesion embodies electrostatic adhesion in soft materials and is required for shape-adaptive and safe grasping of curved objects and delicate materials. In this work, we present a soft electroadhesive fabrication method based on laser scribing graphene oxide on a silicone film, which is cost-effective, facile and green. The method can be used to generate complex electroadhesive patterns without molds or stencils. We then present a 2D finite element model to demonstrate the shape-changing behavior and electric field distributions of a dual-mode parallel dielectric elastomer actuation and coplanar electroadhesion structure. The soft electroadhesive fabrication method based on laser-scribed graphene oxide electrodes and its experimental characterization results, together with its shape-morphing simulation model are expected to enable the wider adoption of soft electroadhesion in future robotics.