This paper presents a novel development for a full Eulerian coupling method between a fluid and capsule with hyperelastic membrane to address a cell adhesion process. The capsule motion in the fluid field and their mechanical interactions are expressed in the Eulerian framework, while solving the capsule adhesion process by stochastic events of ligand-receptor bindings in a discrete level, with using Lagrangian markers distributed on the implicit surface of the capsule. In addition to this, numerical improvements of the full Eulerian method for calculating an interface normal vector and dealing with multiple capsules by introducing the temporarily constructed level set function. A numerical validity of the present development is investigated through a comparison with available numerical data in a validation problem, and a capability for the capsule adhesion is shown in a single capsule adhesion and platelet adhesion in a suspension with blood cells.