Reactions of the carbon-chain radicals are of great importance in the combustion and astrophysical processes. The kinetics of the butadiynyl radical, C4H, has received recent attention. While there has been sufficient knowledge concerning the oxidation of the ethynyl radical, C2H, oxidation of the higher even-numbered members C2nH (n > 1) is hardly known. In this paper, to enrich the C4H-chemistry, we report the first study of the oxidation mechanism of C4H. At the CCSD(T)/aug-cc-pVTZ//B3LYP/6-311++G(d,p)+ZPVE level, the potential energy surface (PES) survey is presented covering various product channels P1(CO + HC3O) (-152.7 kcal/mol), P2(C3H + CO2) (-117.9), P3(HCO + C3O) (-108.5), P4(HC4O+3O) (-45.2), and P5(OH + C4O) (-33.2) accompanied by the master equation rate constant calculations. Despite the similarity in the PES, the kinetics of C4H+3O2 differs dramatically from that of the analogous C2H+3O2 reaction. For the C4H+3O2 reaction, the O-abstraction product P4(HC4O+3O) is almost the exclusive product, whereas the lowest C,O-exchange product P1(CO + HC3O) and other products have little importance. By contrast, the C2H+3O2 reaction favors the C,O-exchange product HCO + CO. Being overall barrierless and mainly associated with the molecular → atomic oxygen conversion, the C4H+3O2 reaction should play an important role in the soot formation and interstellar chemistry where C4H is involved.