The invention discloses a drainage gas recovery method and device of a horizontal well. The drainage gas recovery method comprises the steps of: dividing the whole gas well into a straight well section, a deflecting section and a horizontal section; separating the straight section from the deflecting section and the horizontal section by using a sealer; discharging accumulated liquid in the deflecting section and the horizontal section to the straight well section by adopting a small-diameter pipe; and discharging the accumulated liquid of the straight well section by adopting a conventional process. The drainage gas recovery device comprises oil pipes arranged in the straight well section, the deflecting pipe and the horizontal section, wherein the sealer is arranged on the oil pipe of the straight well section and is used for separating the straight well section from the deflecting section and the horizontal section; a small-diameter pipe with diameter less than that of the oil pipe is connected to the sealer; and the tail end of the small-diameter pipe extends into the horizontal section. By using the energy of the stratum, natural gas and produced liquid in the horizontal section are discharged to the straight well section through the small-diameter pipe, and liquid in the straight well section is lifted out of the shaft to reach the ground by adopting a conventional drainage gas recovery process, so that a relay type drainage gas recovery process is formed, and continuous liquid-carrying production can be realized. The drainage gas recovery method and device have the advantages of high efficiency and long persistence, and is reliable and stabile.