There are a variety of applications for compact toroids(CT) inclding pulse x-rays source, fusion driver etc, and the research of CT acceleration is the foundation of the CT application studies. The theory of CT acceleration was described, based on Whole Acceleration Model, the numerical simulation equations were derived, while the fourth-order Runge-Kutta method was used to calculate these equations. With the parameters of MARADUER in Phillips laboratory and Shiva-Star capacitor set, the CT speedup process in a coaxial accelerator was calculated and the factors affecting acceleration efficiency were analyzed quantitatively. The simulated results show that the efficiency will be improved with the increases of CT mass and accelerator length, but a saturated trend exist, and will be lower with the increases of the resistance, inductance or capacitance for a fix initial energy stored in capacitor.