The lack of turn-off ability makes the spark gap-based Marx generator uncontrollable in terminating the output pulse. In addition, there are some limitations for rise time and voltage gain improvements in the conventional critically-damped Marx design. In this paper, an efficient over-damped design of Marx circuit is proposed, which leads to a shorter rise time as well as a larger voltage gain. A chopping magnetic switch is employed to achieve the desired values of the fall time and full width at half maximum (FWHM). Moreover, adding a DC bias circuit to the magnetic switch provides the ability to adjust the pulse FWHM parameter. Therefore, an output pulse with a shorter rise time, larger voltage gain, and controllable FWHM is achieved. The finite element method is utilized to simulate the structures, and the proposed scheme is evaluated by practical experiments.