This paper discusses and elaborates an analytical model of a multi-stage switched-capacitor (SC) voltage boost converter (VBC) for low-voltage and low-power energy harvesting systems, because the output impedance of the VBC, which is derived from the analytical model, plays an important role in the VBC's performance. In our proposed method, we focus on currents flowing into input and output terminals of each stage and model the VBCs using switching frequency f, charge transfer capacitance C_F, load capacitance C_L, and process dependent parasitic capacitance's parameter k. A comparison between simulated and calculated results showed that our model can estimate the output impedance of the VBC accurately. Our model is useful for comparing the relative merits of different types of multi-stage SC VBCs. Moreover, we demonstrate the performance of a prototype SC VBC and energy harvesting system using the SC VBC to show the effectiveness and feasibility of our proposed design guideline.