Electron acceleration in the plasma wakefield driven by asymmetric laser pulses is investigated analytically. It is found that the asymmetric laser pulse can significantly modify the phase portrait of the electron dynamics and enhance the maximum energy of the accelerated electrons. There exists an optimum ratio of the lengths of the rising and falling segments of the asymmetric laser-pulse. A linear scaling law relating the accelerated electrons' energy and the plasma density is obtained. This result differs from the power-law dependence often associated with symmetric laser pulses.
