Disclosed herein is an apparatus for continuously producing and pelletizing gas hydrates. The apparatus includes a gas supply unit, a water supply unit and a reactor. Gas and water are respectively supplied from the gas supply unit and the water supply unit into the reactor. The gas and water react with each other in the reactor. The reactor includes a dual cylinder unit which forms a gas hydrate in such a way as to squeeze a slurry of reaction water formed by the reaction between the gas and water. The dual cylinder unit includes an upper cylinder, a lower cylinder and a connection pipe which connects the upper cylinder to the lower cylinder. The connection pipe has passing holes through which the reaction water in the reactor flows into and out of the connection pipe.