Hydrogen energy is regarded as an attractive carbon-based fuel alternative due to its advantages of zero pollution and high energy density. Water electrolysis driven by triboelectric nanogenerators (TENGs) has been considered a promising approach for green hydrogen production and the storage of renewable energy in chemicals. However, it is impeded by the slow green hydrogen production rate driven by TENGs and the low value of anodic oxygen product. In this paper, an advanced integrated system of hydrogen evolution reaction coupled with methanol selective oxidation reaction driven by a unidirectional current rotational freestanding triboelectric-layer mode Pulsed-TENG (UDC RF-Pulsed-TENG) after power management was developed, which produced green hydrogen at the cathode while producing the value-added chemical product formic acid at the anode. After power management, a constant voltage of 1.8 V can be applied to the electrochemical cell. Compared with the traditional non-constant voltage power management mode using a switch, the rate of green hydrogen production is increased by 1.68 times. The whole system can realize the green hydrogen production rate of 14.69 µL min−1, with the H2 Faraday efficiency (FE) of 100 %. High value-added formic acid can be prepared simultaneously and the yield of formic acid is 12.50 µg min−1, with the FE of 99.75 %. This research provides an effective method to realize the simultaneous and rapid production of high-purity green hydrogen and value-added formic acid driven by clean energy sources.