The methane (CH4) hydrogen abstraction reaction by linear butadiynyl radical C4H (CCCCH) has been investigated by direct ab,initio dynamics over a wide temperature range of 100-3000 K, theoretically. The potential energy surfaces (PESs) have been constructed at the CCSD(T)/aug-cc-pVTZ//BB1K/ 6-311G(d,p) levels of theory. Two different hydrogen abstraction channels by C-1 and C-4 of C4H ((CCCCH)-C-1-C-2-C-3-H-4) have been considered. The results indicate that the C-1 position of C4H is a more reactive site. The electron transfer behaviors of two possible, channels are also analyzed by quasi-restricted orbital (QRO) in detail. The rate constants calculated by canonical variational transition-state theory (CVT) with the small-curvature tunneling correction (SCT) are in excellent agreement with available experimental values. The normal and three-parameter expressions of Arrhenius rate constants are also provided within 100-3000 K. It is expected to be helpful for further studies on the reaction dynamics behaviors over a wide temperature range where no experimental data is available so far.