This paper reports on a MEMS gravimeter that has a closed-loop system to maintain an ultra-low resonance frequency of 1Hz. The low resonance frequency is attained by using a spring that is the resultant of positive mechanical stiffnesses and negative electrical stiffnesses. Voltage-tunability of the electrical stiffness enables ultra-small and tunable total stiffness. To attain a quick response even at the low resonance frequency, an amplitude monitoring and tuning are done at a higher off-resonance frequency of 330Hz. We demonstrate through simulations that the temperature dependence of the resonance frequency can be eliminated by using closed-loop tuning. To prevent issues caused by the ultra-small stiffness, we employ a force-balanced system that nulls the mass displacement. The sensitivity of the gravimeter is found to be 57V/Gal.