A numerical model of studying the plasma flow dynamics in a rapidly rotatin, axisymmetric magnetosphere has been developed. Starting from a corotating dipole magnetosphere where the plasma density radially decreases as r-3 but the pressure is uniform, we have studied the evolution of the outward plasma flow (centrifugal wind) and the associated conformation of the magnetosphere for two cases; (1) a high pressure case where the corotation speed is smaller than the magnetosonic speed and (2) a low pressure case where the corotation speed exceeds the magnetosonic speed beyond a certain distance. It is found that whether or not the magnetosphere can form a disklike structure depends largely on the pressure distribution in the magnetosphere. It is also confirmed that a super magnetosonic centrifugal wind is generated beyond the critical point where the rotational energy equals the sum of the magnetic and thermal energies. Furthermore, in the case where the disklike structure is formed, a sharp increase in the plasma density appears in the disklike region. Comparisons with the observed Jovian magnetosphere are made.