A waterproof structure (10) of an operating device of a gas stove and a gas stove are provided. The waterproof structure is in the shape of a hollow barrel and includes a snap portion (11) and a sealing portion (12) that are disposed from bottom to top successively along an axial direction of the waterproof structure, the snap portion (11) is connected to the sealing portion (12), and the hardness of the snap portion is higher than the hardness of the sealing portion. In the present invention, the hardness of the snap portion of the waterproof structure is increased, which not only facilitates mounting of the waterproof structure and makes the waterproof structure be more firmly fixed, but also greatly reduces the risk that the waterproof structure is not mounted in place; and the sealing portion with the lower hardness is effectively waterproof. The ingenious combination of the two makes the waterproof structure of the present invention not only have desirable waterproof performance, but also have the advantage of being easy to mount.