In this work, we present a design of a paper-based microfluidic fuel cell (μFC), which employs the spontaneous capillary flow of reactant solutions in a filter paper to accomplish passive conveyance of the fuel and oxidant. This self-pumping device uses methanol vapor as a fuel. The gas phase in the microfluidic fuel cell increases the fuel supply to the anode due to a higher diffusion coefficient of 1.5 × 10−5 m2 s−1 compared with 5 × 10−9 m2 s−1 for liquid phase. An air-breathing cathode is incorporated to paper-based μFC through which atmospheric oxygen is continuously supplied. The paper-based μFC performance is studied by polarization curves and chronoamperometry to determinate the power output and stability. Peak power of 1.49 mW and a stable current of 1.35 mA at 0.35 V for 28 h can be achieved with this prototype under room temperature. To interpret the device performance a numerical model is developed and validated with the experimental polarization curve. The fuel and oxidant concentration profiles in the electrodes from the model demonstrates a constant species availability at the cathode and anode and explains the stable current obtained in the experimental measurements. Subsequently, a stack of four MμFCFP was developed and evaluated in both series and parallel connections. In the parallel configuration, a maximum open circuit potential (OCP) of 0.69 V with a maximum current and power output of 34.53 mA and 4.14 mW are delivered, respectively. Conversely, in the series connection, a total current of 7.35 mA, an OCP of 2.39 V and a maximum power of 3.57 mW are reached. As a proof of concept, the stack successfully operates a 3 green LEDs array, each requiring a 2.1–2.5 V and 4.2–5 mW power to function, for a continuous duration of 3 h.