Electron acceleration in plasma driven by circular polarized ultraintense laser with asymmetric pulse are investigated analytically and numerically in terms of oscillation-center Hamiltonian formalism. Studies include wakefield acceleration, which dominates in blow-out or bubble regime and snow-plow acceleration which dominates in supra-bubble regime. By a comparison with each other it is found that snow-plow acceleration has lower acceleration capability. In wakefield acceleration, there exists an obvious optimum pulse asymmetry or/and pulse lengths that leads to the high net energy gain while in snow-plow acceleration it is insensitive to the pulse lengths. Power and linear scaling laws for wakefield and snow-plow acceleration respetively are observed from the net energy gain depending on laser field amplitude. Moreover, there exists also an upper and lower limit on plasma density for an effective acceleration in both of regimes.