To effectively reduce a situation in which an over-rotation of an expander occurs or the expander becomes a load on an engine at the time of a stop of a Rankine cycle in an exhaust heat recovery device provided with the Rankine cycle that recovers exhaust heat of an engine. A pressure difference ΔP between a high-pressure side and a low-pressure side of the Rankine cycle is obtained when the Rankine cycle is stopped (S1), a waiting time Ta is set (calculated) based on the obtained pressure difference ΔP (S2). Then, a bypass valve is opened to allow a refrigerant to circulate while bypassing the expander (S3), and then an electromagnetic clutch is disengaged when the waiting time Ta has elapsed to block transmission of power between the expander and the engine (S4, S5).