The electron acceleration mechanism in a wake of the plasma with a variety of adiabatically attenuating density modes is checked by numerical simulation. The simulation results prove that the new electron acceleration mechanism owing to the density attenuating is operated well,and the properly choice of the density attenuating mode can greatly improve the quality of accelerated electrons beam. And the results indicate that the efficiency of the electron acceleration mechanism in a wake of the plasma with a variety of adiabatically attenuating density modes is not dependent on the very high intensity of the laser. Experimental verification is convenient.