A novel charge pump, Capacitance Varying Charge Pump (CVCP) is proposed. This charge pump is composed of variable capacitors and rectifiers, and the charge transfer is attained by changing the capacitance values in a manner similar to peristaltic pumps. The analysis of multi-stage CVCP reveals that the output voltage is exponentially dependent on the stage number. Thus, compared with the Dickson charge pump, this charge pump has an advantage in generating high voltages with small stages. As a practical example of CVCP, we present an implementation realized by a MEMS (Micro-Electro-Mechanical Systems) technology. Here, the variable capacitor is enabled by a comb-capacitor attached to a high-quality factor resonator. As the rectifier, a PN-junction diode formed in the MEMS layer is used. Simulations including the mechanical elements are carried out for this MEMS version of CVCP. The simulation results on the output voltage and load characteristics are shown to coincide well with the theoretical estimations. The MEMS CVCP is suited for MEMS devices and vibration energy harvesters.