A gas injector, for injecting gaseous fuel, includes a valve body having a first valve seat and a second valve seat, and a closing element, which has a first sealing region, a second sealing region, a hollow region, which is delimited by a bottom and a wall, and an outlet opening configured in the bottom, the first valve seat sealing at the first sealing region, and the second valve seat sealing at the second sealing region, and at least one through opening being provided in the wall of the closing element, so that the gaseous fuel is able to be expelled both from the inner hollow region and the outer region of the closing element.