This paper presents a design-oriented analysis on the voltage stability and the transient fault current limitation of voltage-controlled modular multilevel converter (MMC) with L-filters. First, a dual-loop voltage control based on the L-filter plant is systematically designed, where the upper limits of controller parameters to ensure the small-signal stability are identified. Then, considering the transient current limitation during faults, the lower boundaries of inner current controller parameters are derived. Within the region of allowed controller parameters, the optimization is further made to minimize the closed-loop output impedance of MMC, which enhances the output voltage stiffness against the load current disturbance. Lastly, time-domain simulations corroborate the theoretical analysis.