Recently, omnidirectional mobile robots with holonomic property have been studied actively. We have already developed a holonomic and omnidirectional mobile robot which consists of two active dual-wheel caster assemblies and also derived the kinematic models for the assembly and the mobile robot. In this paper, we further derive a dynamic model for the mobile robot by using the forces acting on the steering axis and construct a resolved acceleration control system based on the model to realize a dynamic control for the mobile robot. An experiment using a prototype robot is performed to prove the validity of the model and the effectiveness of the control system.