PROBLEM TO BE SOLVED: To effectively recover an olefin gas, hydrogen, and BTX from a waste plastic. SOLUTION: This method comprises a pretreatment step (I) for separating a waste plastic into a polyolefin plastic and other plastics; a thermal decomposition step (II) for thermally decomposing the polyolefin plastic; a catalytic decomposition step (III) wherein 2-4C olefins are formed from a thermal decomposition gas 5 (generated at step II) by the action of a boron-containing silicate catalyst 7 of a first catalytic decomposition section 8 and BTX and hydrogen are formed by the action of a gallium-containing silicate catalyst 9 of a second catalytic decomposition section 10; a high-boiling-point component separation step (IV) for separating a high-boiling-point component from a gas 13 coming out of step III; and a gas-liquid separation step (V) wherein the gas 13 freed of the high-boiling-point component is cooled to be separated into a gas phase 16 mainly comprising a 2-4C olefin gas and hydrogen and a liquid phase 17 mainly comprising BTX.