A frequency-tuning method with a high tuning sensitivity is difficult to control precisely or even cause the pull-in phenomenon before attaining the desired frequency. Here, the sensitivity is defined by the rate of change of the frequency with respect to the bias voltage. In this paper, a two-stage tuning technique is proposed to overcome fundamental challenges of MEMS vibration energy harvesting from low-frequency applications. The technique can significantly reduce the tuning sensitivity in comparison with previous tuning methods. In our particular example designs, when the frequency is tuned from 1 kHz to 50 Hz, a traditional tuning approach has a sensitivity of 495 Hz/V, while that of the proposed tuning approach is 18 Hz/V under the same design constraint. The effects of the tip capacitance are taken into account when investigating the pull-in phenomenon and estimating the theoretical lowest tunable frequency. The findings can provide a further guideline towards the optimal design of MEMS vibration energy harvesters operating at low-frequency ranges.