The invention discloses a gasification system of garbage and organic waste and a device thereof, and relates to a garbage treatment device. The gasification system mainly consists of a blast drier, a gas phase circulation gasification furnace, a dusting/purification device, a compressor, a gas receiver and connection pipelines, wherein, the gasification furnace is equipped with a baking zone, a pyrolysis zone, a first gasification zone, a second gasification zone, a burnout zone and a heat storage chamber, a recirculating blower and a recirculating wind pipeline form a gas phase circulation loop outside the furnace. In the system, a discharge port of the blast drier is connected to a feed inlet of the gasification furnace, a synthesis gas output interface of the gasification furnace is connected to the dusting/purification device by an induced draft fan, the dusting/purification device is connected to the compressor, and the compressor is connected to the gas receiver. The system utilizes a technical measure of arranging the heat storage chamber in a gas phase circulation gasification furnace to enhance gasification rate and quality of refuse fuel and decompose dioxin with severe toxicity and eliminate coke tar, convert garbage and organic waste into secondary clean energy which comprises producer city coal gas, hydrogen, methanol and dimethyl ether liquefied gas.